# TTT13: Leicester

Department of Mathematics and Computer Science, University of Leicester.

The meeting was devoted to the work of Leary and Nucinkis on the proper classifying space of certain infinite discrete groups. It included the usual time for participant discussion.

## Date

9 March 1998

## Speakers

Ian Leary (Southampton)

Can Kan-Thurston be done properly?

Brita Nucinkis (Southampton)

Can Eilenberg-Ganea be done properly?

## Abstract

The Kan-Thurston theorem and the Eilenberg-Ganea theorem are theorems about BG, a classifying space for principal G-bundles. They say respectively, that any connected CW-complex has the same homology as a BG for some G, and that if G has finite cohomological dimension, there is a finite dimensional BG.

The titles of the talks are intended to ask: Is there an analogous theorem for \underline{B}G, a classifying space for proper G-bundles (the space that features in the Baum-Connes conjecture, and in the definition of relative cohomology). The answers are "yes" and "maybe".

The analogue of Kan-Thurston is significantly easier than the original, and is joint work of Leary and Nucinkis. The analogue of Eilenberg-Ganea is more subtle, and only partial results are known via the work of Kropholler-Mislin and of Nucinkis.

## Further information

The meeting was partially supported by a Scheme 3 grant from the London Mathematical Society.