Nullification functors and the homotopy type of the classifying space
for proper bundles

Ram'on J. Flores

Departamento de Matem'aticas,
Universidad Aut'onoma de Barcelona,
E-08193 Bellaterra,
Spain

E-mail address: ramonj@mat.uab.es

 Abstract. Let G be a discrete group. In this note we build a bridge
 between the homotopy theory of BG and the theory of proper G-actions,
 by showing that under mild restrictions, the classifying space for
 proper G-bundles has the homotopy type of the W-nullification of BG for
 some space W. This allows us to use properties of the localization
 functors to obtain spaces that are homotopy equivalent to this "proper"
 classifying space for a wide range of groups, and on the other hand, we
 take profit of the existence of well-known geometrical and
 finite-dimensional models of it for some infinite groups to deduce
 homotopical information about the p-primary part of their classifying
 spaces.