Equivariant E-theory for C*-algebras

Erik Guentner, Nigel Higson, Jody Trout

Research output: Contribution to journalArticle

24 Scopus citations

Abstract

Let A and B be C*-algebras which are equipped with continuous actions of a second countable, locally compact group G. We define a notion of equivariant asymptotic morphism, and use it to define equivariant E-theory groups EG(A, B) which generalize the E-theory groups of Connes and Higson. We develop the basic properties of equivariant E-theory, including a composition product and six-term exact sequences in both variables, and apply our theory to the problem of calculating K-theory for group C*-algebras. Our main theorem gives a simple criterion for the assembly map of Baum and Connes to be an isomorphism. The result plays an important role in recent work of Higson and Kasparov on the Baum-Connes conjecture for groups which act isometrically and metrically properly on Hilbert space.

Original languageEnglish (US)
JournalMemoirs of the American Mathematical Society
Volume148
Issue number703
StatePublished - Nov 1 2000

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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