Complex Topological K-Theory

The first contemporary introduction to topological K-theory. Self-contained: no background in algebraic topology is necessary.

Efton Park (Author)

9780521856348, Cambridge University Press

Hardback, published 13 March 2008

218 pages, 43 b/w illus. 43 exercises
23.3 x 15.7 x 1.2 cm, 0.428 kg

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

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.

1. Preliminaries
2. K-Theory
3. Additional structure
4. Characteristic classes
Bibliography
Symbol index
Subject index.

Subject Areas: Algebraic topology [PBPD], Topology [PBP]