DIFFERENTIAL TOPOLOGY VICTOR GUILLEMIN ALAN POLLACK AMS CHELSEA PUBLISHING American Mathematical Society • Providence, Rhode Island Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms DIFFERENTIAL TOPOLOGY Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms http://dx.doi.org/10.1090/chel/370 DIFFERENTIAL TOPOLOGY VICTOR GUILLEMIN ALAN POLLACK AMS CHELSEA PUBLISHING American Mathematical Society # Providence, Rhode Island FO UN 8 DED 1 SOCIETY Α Γ ΕΩ ΜΕ ΤΡΗΤΟΣ ΜΗ ΕΙΣΙΤΩ R AME ICAN L HEMATIC AT A M 88 Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms 2000 Mathematics Subject Classification. Primary 53Cxx, 57Rxx, 58Axx. For additional information and updates on this book, visit www.ams.org/bookpages/chel-370 Library of Congress Cataloging-in-Publication Data Guillemin, Victor, 1937– Differential topology / Victor Guillemin, Alan Pollack. p. cm. Originally published: Englewood Cliffs, N.J. : Prentice-Hall, 1974. Includes bibliographical references and index. ISBN 978-0-8218-5193-7 (alk. paper) 1. Differential topology. I. Pollack, Alan, 1946– II. Title. QA613.6.G84 2010 514.72—dc22 2010011053 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy a chapter for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication is permitted only under license from the American Mathematical Society. Requests for such permission should be addressed to the Acquisitions Department, American Mathematical Society, 201 Charles Street, Providence, Rhode Island 02904-2294 USA. Requests can also be made by e-mail to [email protected]. c 1974 held by the American Mathematical Society. All rights reserved. Reprinted by the American Mathematical Society, 2010, 2014. Printed in the United States of America. ∞ The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. Visit the AMS home page at http://www.ams.org/ 10 9 8 7 6 5 4 3 2 19 18 17 16 15 14 Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Prefaces , xi xv xvii Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Preface to the AMS Chelsea Edition We are deeply grateful to the AMS for reissuing Differential Topology as part of its AMS Chelsea Book Series. Our elementary introduction to topology via transversality techniques has managed to stay in print for most of the thirtysix years since its original appearance, and we would like to thank Edward Dunne and his colleagues in Providence for ensuring its continuing availability (knock on wood) for the next thirty-six years. The techniques it highlights have, in some sense, a very 1970’s flavor. The quixotic hopes of that decade, that singularity theory and catastrophe theory (of whose catastrophic demise the less said the better) would have a revolutionary impact on physics, chemistry, biology, economics, game theory, and investment strategies in the stock market, have proved largely unfounded. However, we have been pleased to find that our students today are, just as were the students of three decades ago, happy with the visceral, down-to-earth approach to topology espoused by books like ours and Milnor’s wonderful Topology from a Differential Viewpoint. We hope (again knock on wood) that whatever the fashions in mathematics of the next thirty-six years, this will continue to be the case. Victor Guillemin Alan Pollack ix Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms xi Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms xii Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms xiii Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms xv Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms xvi Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms xvii Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms xviii Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms http://dx.doi.org/10.1090/chel/370/01 Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. 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License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms http://dx.doi.org/10.1090/chel/370/02 Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. 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License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms http://dx.doi.org/10.1090/chel/370/03 Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms http://dx.doi.org/10.1090/chel/370/04 Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms http://dx.doi.org/10.1090/chel/370/05 Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms http://dx.doi.org/10.1090/chel/370/06 Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms CHEL/370.H Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms Licensed to Univ Nac Autonoma de Mexico. Prepared on Mon Oct 4 09:53:37 EDT 2021for download from IP 132.248.9.8/132.248.9.41. License or copyright restrictions may apply to redistribution; see https://www.ams.org/publications/ebooks/terms