Homology, Homotopy and Applications

Volume 8 (2006)

Number 2

Homotopy invariance in E-theory

Pages: 29 – 49

DOI: https://dx.doi.org/10.4310/HHA.2006.v8.n2.a2

Author

Klaus Thomsen (Institut for matematiske fag, Ny Munkegade, Aarhus, Denmark)

Abstract

We introduce equivalence relations among asymptotic homomorphisms that in general are stronger than homotopy, but which we show are equivalent to homotopy when the domain is a suspended $C*$-algebra. As an application, we show that the $E$-theory of Connes and Higson can be realized as a special case of Kasparov’s KK-theory.

Keywords

$E$-theory, asymptotic homomorphisms

2010 Mathematics Subject Classification

19K35, 46L85

Published 1 January 2006