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Diferential topology

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DIFFERENTIAL
TOPOLOGY
VICTOR GUILLEMIN
ALAN POLLACK
AMS CHELSEA PUBLISHING
American Mathematical Society • Providence, Rhode Island
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DIFFERENTIAL
TOPOLOGY
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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
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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 reprint-permission@ams.org.
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
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Prefaces
, xi
xv
xvii
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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
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xi
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xii
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xiii
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xv
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xvi
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xvii
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xviii
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http://dx.doi.org/10.1090/chel/370/01
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http://dx.doi.org/10.1090/chel/370/05
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http://dx.doi.org/10.1090/chel/370/06
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CHEL/370.H
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