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Complex Topological K-Theory

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Hardcover | 13 March 2008

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Hardcover
220 Pages

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22.86 x 15.24 x 1.42

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Topological K-theory is a key tool in topology, differential geometry and index theory, yet this is the first contemporary introduction for graduate students new to the subject. No background in algebraic topology is assumed; the reader need only have taken the standard first courses in real analysis, abstract algebra, and point-set topology. The book begins with a detailed discussion of vector bundles and related algebraic notions, followed by the definition of K-theory and proofs of the most important theorems in the subject, such as the Bott periodicity theorem and the Thom isomorphism theorem. The multiplicative structure of K-theory and the Adams operations are also discussed and the final chapter details the construction and computation of characteristic classes. With every important aspect of the topic covered, and exercises at the end of each chapter, this is the definitive book for a first course in topological K-theory.

Industry Reviews

'... the presentation is very nice and the book can be strongly recommended.' European Mathematical Society Newsletter

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Preface	p. ix
Preliminaries	p. 1
Complex inner product spaces	p. 1
Matrices of continuous functions	p. 5
Invertibles	p. 10
Idempotents	p. 17
Vector bundles	p. 21
Abelian monoids and the Grothendieck completion	p. 29
Vect(X) vs. Idem(C(X))	p. 31
Some homological algebra	p. 39
A very brief introduction to category theory	p. 43
Notes	p. 47
Exercises	p. 47
K-theory	p. 51
Definition of K⁰(X)	p. 51
Relative K-theory	p. 54
Invertibles and K^-1	p. 62
Connecting K⁰ and K^-1	p. 69
Reduced K-theory	p. 76
K-theory of locally compact topological spaces	p. 78
Bott periodicity	p. 83
Computation of some K groups	p. 103
Cohomology theories and K-theory	p. 107
Notes	p. 108
Exercises	p. 109
Additional structure	p. 111
Mayer-Vietoris	p. 111
Tensor products	p. 114
Multiplicative structures	p. 119
An alternate picture of relative K⁰	p. 130
The exterior algebra	p. 141
Thom isomorphism theorem	p. 147
The splitting principle	p. 157
Operations	p. 166
The Hopf invariant	p. 170
Notes	p. 173
Exercises	p. 173
Characteristic classes	p. 176
De Rham cohomology	p. 176
Invariant polynomials	p. 181
Characteristic classes	p. 187
The Chern character	p. 196
Notes	p. 200
Exercises	p. 201
References	p. 203
Symbol index	p. 204
Subject index	p. 206
Table of Contents provided by Ingram. All Rights Reserved.

Complex Topological K-Theory

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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