Sharp homology decompositions for classifying
                 spaces of finite groups

                        W. Dwyer
                  University of Notre Dame

Suppose that G is a finite group. A homology decomposition for BG is a
way of constructing BG up to mod p homology as a homotopy colimit of
classifying spaces of subgroups K of G.  The decomposition is said to
be sharp if the mod p homology spectral sequence associated to the
homotopy colimit collapses to give an isomorphism between the H^*BG
and colim H^*BK. We develop techniques for showing that a
decomposition is sharp, and apply the techniques to a number of
examples.

(Preprint as of 6/96)