Topological and bivariant K-theory
Joachim Cuntz, Ralf Meyer, Jonathan M. Rosenberg · 2007
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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. We describe a bivariant K-theory for bornological algebras, which provides a vast generalization of topological K-theory. In addition, we discuss other approaches to bivariant K-theories for operator algebras. As applications, we study 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.
Book details
- Year
- 2007
- Language
- English
- Publisher
- Birkhäuser Basel
- Editions
- 3
- Pages
- 262
- ISBN
- 9783764383985
Data source: Wikidata
