num_pages: 274
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.
language: English
title: Topological and Bivariant K-Theory
publisher: Birkhäuser