Topological and Bivariant K-Theory
Author | : Joachim Cuntz |
Publisher | : Springer Science & Business Media |
Total Pages | : 268 |
Release | : 2007-10-04 |
ISBN-10 | : 9783764383992 |
ISBN-13 | : 3764383992 |
Rating | : 4/5 (92 Downloads) |
Book excerpt: 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.