Sharp homology decompositions for classifying
spaces of finite groups
W. Dwyer
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.