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.
- ISBN13 9783764383985
- Publish Date 19 July 2007
- Publish Status Active
- Publish Country CH
- Imprint Birkhauser Verlag AG
- Edition 2007 ed.
- Format Paperback
- Pages 262
- Language English