Topological and Bivariant K-Theory

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 a...

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Main Authors: Cuntz, Joachim, Meyer, Ralf (Author), Rosenberg, Jonathan M. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Basel Birkhäuser Basel 2007, 2007
Series:Oberwolfach Seminars
Subjects:
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
Summary: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
Physical Description:XII, 262 p online resource
ISBN:9783764383992