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|a 9783764383992
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| 100 |
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|a Cuntz, Joachim
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| 245 |
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|a Topological and Bivariant K-Theory
|h Elektronische Ressource
|c by Joachim Cuntz, Jonathan M. Rosenberg
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| 250 |
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|a 1st ed. 2007
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| 260 |
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|a Basel
|b Birkhäuser
|c 2007, 2007
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| 300 |
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|a XII, 262 p
|b online resource
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| 505 |
0 |
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|a 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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| 653 |
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|a K-Theory
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| 653 |
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|a Topology
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| 653 |
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|a K-theory
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| 700 |
1 |
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|a Rosenberg, Jonathan M.
|e [author]
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| 041 |
0 |
7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b Springer
|a Springer eBooks 2005-
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| 490 |
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|a Oberwolfach Seminars
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| 028 |
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|a 10.1007/978-3-7643-8399-2
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| 856 |
4 |
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|u https://doi.org/10.1007/978-3-7643-8399-2?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
0 |
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|a 512.66
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| 520 |
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|a 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
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