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Topological and bivariant K-theory

Author: Joachim Cuntz; Ralf Meyer; Jonathan M Rosenberg
Publisher: Basel ; Boston : Birkhäuser, ©2007.
Series: Oberwolfach seminars, 36.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Cuntz, Joachim, 1940-
Topological and bivariant K-theory.
Basel ; Boston : Birkhäuser, ©2007
(DLC) 2007929010
(OCoLC)141385291
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Joachim Cuntz; Ralf Meyer; Jonathan M Rosenberg
ISBN: 9783764383992 3764383992 3764383984 9783764383985
OCLC Number: 191454027
Description: 1 online resource (xi, 262 pages) : illustrations.
Contents: 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.
Series Title: Oberwolfach seminars, 36.
Responsibility: Joachim Cuntz, Ralf Meyer, Jonathan M. Rosenberg.
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Abstract:

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  Read more...

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