Topological and Bivariant K-Theory
- ISBN-10
- 3764383992
- ISBN-13
- 9783764383992
- Category
- Mathematics
- Pages
- 262
- Language
- English
- Published
- 2007-10-04
- Publisher
- Springer Science & Business Media
- Authors
- Joachim Cuntz, Jonathan M. Rosenberg
Description
Topological K-theory is one of the most important invariants for noncommutative algebras. 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.
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