William Browder, Lecture 5

A homological approach to problems of compact group actions:
The workshop; constructions of actions, questions.

Speaker: William Browder. Lecture 5.

Abstract: A method of consructing actions using Postnikov towers is used to construct counterexamples to many what would otherwise have led to very useful methods. Let X be a free G space (G elementary abelian p-group) with the properties: 

a) G acts as the identity in homology

b) Rank of H*(X;F_p) = s < oo (infinity)

c)All positive dimensional cup products are zero.

For rank G = 2 , the minimum such s is 6.
In general is there a formula relating minimal rank of homology,
rank of free symmetry (rank G) and minimal cup product length?
Question: Suppose G acts trivially on H*(X), does G/K act trivially on H*(X/K) for K
a subgroup of G?