文档介绍：Graduate Texts in Mathematics 82
Eriiroriill Bnrrrd
F. W. Gchring P. (Managing Editor)
C. C. Moore
Raoul Bott
Loring W. Tu
Differential Forms in
Algebraic Topology
With 92 Illustrations
Springer-Vcrlag
New York Heidelberg Berlin
Raoul Hott Loririg W. l'u
Llepartn~ent01' Mathematics Dcpnrt~ncntof Mathcrnatics
Harvard Univcrsity Utiiversity of Michigan
Cambridge, Massachusetts 02138 Ann Arbor, Michigan 48 109
USA USA
Board
P. R. Halmov 17. W. Geliring C. C. Moore
Murrrigir~gEditor Department of Departinent of
Department of Mathem~tics Mntl~ematics
~atics U~liversityof Michigan University of Califorilia
I~idianaUniversity Ann Arbor, MI 48109 Berkeley, CA 93720
UIootning~un,IN 47401 USA USA For
USA Phyllis Bott
and
- Lichld and Il'suchih Tu
AMS tio~is:57 Rxx, 58 Axx, 14 1:40
Libriiry of Congress Cataloging in Piiblicatiun Data
Rot(, Raoul, 1924-
DiKerential forms in algcbraic topo!ogy.
(Graduate tcxts ir~rnathemaiics; 82)
Bibliography: y.
lncl~tdesindex.
1. tial topology. 2. Algebraic
topology. 3. tial Curlus. I. Tu,
Loring W. 11. Tirle. 111. Series.
514'.72 81-9172
A ACR2
a 1982 by Springer-Verlag New Yurk Inc.
All rights reserved. Nu part of this book may be tratlslatcd or reproduced in any
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ISBN 0-387-9061 3-4 Sprirlgcr-Verlag New York Heidelberg Heslin
ISBN 3-540-30613-4 Springer-Verlag Berlin Heidelbcrg New York
Preface
Tho guiding principle in this book is to use differential forms as an aid it1
exploring some of the less digestible aspects of algebraic topology. Accord-
ingly, we move primarily in the realrn of smooth manifolds and usc the
de Rl~amtheory as n prototype of all of cohamology. For applications to
hon~otopythcory we also discuss by way of analogy cohomology