Characteristic Classes

Front Cover
Princeton University Press, 1974 - Mathematics - 330 pages
6 Reviews
The theory of characteristic classes began in the year 1935 with almost simultaneous work by Hassler Whitney in the United States and Eduard Stiefel in Switzerland. Stiefel's thesis, written under the direction of Heinz Hopf, introduced and studied certain 'characteristic' homology classes determined by the tangent bundle of a smooth manifold.
  

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Review: Characteristic Classes. (Am-76)

User Review  - Jon Paprocki - Goodreads

Fantastically written! In addition to teaching me many new topics, my understanding of ideas that I thought I had achieved level 3 knowledge of, such as the CW complex, were improved by this book ... Read full review

Review: Characteristic Classes. (Am-76)

User Review  - Jamie - Goodreads

I just didn't get it. Maybe I didn't invest myself into it enough. Davis and Kirk say that every mathematician should read this book. Whatever (ie I disagree). Read full review

Contents

Preface 1 Smooth Manifolds
3
2 Vector Bundles
13
3 Constructing New Vector Bundles Out of Old
25
4 StiefelWhitney Classes
37
5 Grassmann Manifolds and Universal Bundles
55
6 A Cell Structure for Grassmann Manifolds
73
7 The Cohomology Ring HGn Z2
83
8 Existence of StiefelWhitney Classes
89
15 Pontrjagin Classes
173
16 Chern Numbers and Pontrjagin Numbers
183
17 The Oriented Cobordism Ring fl
199
18 Thom Spaces and Transversality
205
19 Multiplicative Sequences and the Signature Theorem
219
20 Combinatorial Pontrjagin Classes
231
Epilogue
249
Singular Homology and Cohomology
257

9 Oriented Bundles and the Euler Class
95
10 The Thom Isomorphism Theorem
105
11 Computations in a Smooth Manifold
115
12 Obstructions
139
13 Complex Vector Bundles and Complex Manifolds
149
14 Chern Classes
155
Bernoulli Numbers
281
Connections Curvature and Characteristic Classes
289
Bibliography
315
Index
325
Copyright

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