Title: ``The type of the classifying space for a family of subgroups''

Author: Wolfgang Lueck

AMS-classification number: 55R35

Address:
Wolfgang Lueck 
Fachbereich Mathematik und Informatik
Westf\"alische Wilhelms-Universitaet Muenster
Einsteinstr. 62
48149 M\"unster
Germany

Abstract:
The classifying space E(G,F) for a family F of subgroups of a group G
is defined up to G-homotopy as a G-CW-complex E(G,F) such that E(G,F)^H 
is contractible if H belongs to F and is empty otherwise.  The space 
E(G,F) occurs in the Baum-Connes-Conjecture, The Isomorphism-Conjecture in 
algebraic K-theory and L-theory of Farrell and Jones and in the version of
the Atiyah-Segal-Completion-Theorem for proper cocompact actions of 
discrete groups. We investigate  the question whether there is a 
finite-dimensional G-CW-model, a finite
G-CW-model or a G-CW-model of finite type for E(G,F) focusing on the case 
where F is the family FIN of finite subgroups.