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Topological and Bivariant K-Theory / by Joachim Cuntz, Jonathan M. Rosenberg
(Oberwolfach Seminars. ISSN:22965041 ; 36)
版 | 1st ed. 2007. |
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出版者 | Basel : Birkhäuser Basel : Imprint: Birkhäuser |
出版年 | 2007 |
本文言語 | 英語 |
大きさ | XII, 262 p : online resource |
著者標目 | *Cuntz, Joachim author Rosenberg, Jonathan M author SpringerLink (Online service) |
件 名 | LCSH:K-theory LCSH:Topology FREE:K-Theory FREE:Topology |
一般注記 | 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 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 HTTP:URL=https://doi.org/10.1007/978-3-7643-8399-2 |
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Springer eBooks | 9783764383992 |
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EB00231429 |
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