# Thirteenth meeting of the Transpennine Topology Triangle

## Department of Mathematics and Computer Science

University of Leicester

9th March 1998

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

## Programme

Coffee will be available from 10.30 am in F9, and the first talk will probably
start at 11.30; talks in G4 of the Mathematics Building.

- 11.30 am Ian Leary (Southampton)

Can Kan-Thurston be done properly?

- 3.00 pm Brita Nucinkis (Southampton)

Can Eilenberg-Ganea be done properly?

Arrangements for a meal or drink afterwards will be made on the day.

## 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.

Anyone who wishes to participate is welcome: we shall operate the
usual arrangements for assistance with travel expenses. We expect
to assemble for tea and coffee
from 11.00 am until the first talk.

Tea and Coffee will be served in
the common room.

For further information email John Hunton
jrh7@mcs.le.ac.uk
(or John Greenlees
j.greenlees@sheffield.ac.uk or
Nige Ray
nige@ma.man.ac.uk) if you are interested, so we can make
approximately the right amount of tea and coffee.

## How to get there

It is a short walk from the rail station. See
maps and how to get to Leicester University

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

## Escape routes

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