Isaac Newton Institute for Mathematical Sciences

On homotopy non-invertibility of C*-extensions

13th December 2006

Author: V Manuilov (Moscow State University)

Abstract

The Brown-Douglas-Fillmore functor Ext classifying extensions of C*-algebras is so nice for nuclear arguments because of two features: it has an abelian group structure and it is homotopy invariant. Unfortunately, beyond the nuclear case both these features do not hold in general. To avoid homotopy non-invariance, we considered another functor, Ext_h, of homotopy classes of extensions and checked it for being a group. It turned out that the deficiency of having non-invertible elements persists in Ext_h as well. The technique is based on a modification of S. Wassermann's ideas and our examples of homotopy non-invertible extensions are related to property T groups. This is a joint work with K. Thomsen (Aarhus).