Topological and bivariant K-theory
著者
書誌事項
Topological and bivariant K-theory
（Oberwolfach seminars, v. 36）
Birkhäuser, c2007
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注記
Includes bibliographical references (p. [241]-247) and index
内容説明・目次
内容説明
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.
目次
The elementary algebra of K-theory.- Functional calculus and topological K-theory.- Homotopy invariance of stabilised algebraic K-theory.- Bott periodicity.- The K-theory of crossed products.- Towards bivariant K-theory: how to classify extensions.- Bivariant K-theory for bornological algebras.- A survey of bivariant K-theories.- Algebras of continuous trace, twisted K-theory.- Crossed products by ? and Connes' Thom Isomorphism.- Applications to physics.- Some connections with index theory.- Localisation of triangulated categories.
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