Download or read book Topological and Bivariant K-Theory written by Joachim Cuntz and published by Springer Science & Business Media. This book was released on 2007-10-04 with total page 268 pages. Available in PDF, EPUB and Kindle. 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.