Topological and Bivariant K-theory

by Cuntz, Joachim; Meyer, Ralf; Rosenberg, Jonathan M.

• ISBN13: 9783764383985
• ISBN10: 3764383984
• Format: Paperback
• Copyright: 2007-09-03
• Publisher: Birkhauser

Summary

Topological K-theory is one of the most important invariants for noncommutative algebras equipped with a suitable topology or bornology. Bott periodicity, homotopy invariance, and various long exact sequences distinguish it from algebraic K-theory.This book describes a bivariant K-theory for bornological algebras, which provides a vast generalization of topological K-theory. In addition, it details other approaches to bivariant K-theories for operator algebras. The book studies a number of applications, including K-theory of crossed products, the Baum-Connes assembly map, twisted K-theory with some of its applications, and some variants of the Atiyah-Singer Index Theorem.

Table of Contents

The elementary algebra of K-theory	p. 1
Functional calculus and topological K-theory	p. 19
Homotopy invariance of stabilised algebraic K-theory	p. 45
Bott periodicity	p. 63
The K-theory of crossed products	p. 75
Towards bivariant K-theory: how to classify extensions	p. 91
Bivariant K-theory for bornological algebras	p. 123
A survey of bivariant K-theories	p. 141
Algebras of continuous trace, twisted K-theory	p. 173
Crossed products by R and Connes' Thorn Isomorphism	p. 185
Applications to physics	p. 195
Some connections with index theory	p. 203
Localisation of triangulated categories	p. 225
Table of Contents provided by Blackwell. All Rights Reserved.