TITLE: "Homology equivalences inducing an epimorphism on 
             the fundamental group"

AUTHORS: 
Jose L. Rodriguez
Universitat Autonoma de Barcelona
E--08193 Bellaterra, Spain
http://mat.uab.es/jlrodri

Dirk Scevenels
Departement Wiskunde, Katholieke Universiteit Leuven, 
Celestijnenlaan 200 B, 
B--3001 Heverlee, Belgium

ABSTRACT: 
Quillen's plus construction is a topological construction 
that kills the maximal perfect subgroup of the fundamental 
group of a space without changing the integral homology 
of the space. In this paper we show that there is a 
topological construction that, while leaving the integral 
homology of a space unaltered, kills even the intersection 
of the transfinite lower central series of its fundamental 
group. Moreover, we show that this is the maximal subgroup 
that can be factored out of the fundamental group without 
changing the integral homology of a space.