Topological and Bivariant K-Theory

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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Bibliographic Details
Main Authors: Cuntz, Joachim (Author), Meyer, Ralf (Author), Rosenberg, Jonathan M. (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic eBook
Language:English
Published: Basel : Birkhäuser Basel, 2007.
Series:Oberwolfach Seminars ; 36
Subjects:
Mathematics.
K-theory.
Topology.
K-Theory.
Online Access:Full Text via HEAL-Link
Table of 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.

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