Title:      Classifying spaces for proper actions of locally-finite groups 

Authors:    Warren Dicks, Peter H. Kropholler, Ian J. Leary and Simon Thomas

Addresses and email:      

W. Dicks 
Departament de Matem\`atiques,
Universitat Aut\`onoma de Bar\-ce\-lo\-na,
E-08193 Bella\-terra (Barcelona), Spain

P. H. Kropholler 
School of Mathematical Sciences,
Queen Mary, University of London,
Mile End Road, 
London E1 4NS, United Kingdom

I. J. Leary 
Faculty of Mathematical Studies,
University of Southampton,
Southampton SO17 1BJ, United Kingdom

S. Thomas 
Department of Mathematics,
Rutgers University,
New Brunswick, N.~J.~08903, USA


Abstract:  For each finite ordinal $n$ and each locally-finite group $G$ of 
cardinality $\aleph_n$, we construct an $(n+1)$-dimensional model for
the classifying space for proper $G$-actions. We use this complex to 
obtain information about the cohomology of $G$ with free
coefficients. Our techniques also give information about the location
of large free abelian groups within Kropholler's hierarchy.