Title: On Nilpotent Ideals in the Cohomology Ring of a Finite 
Group.

Authors: Jonathan Pakianathan & Ergun Yalcin 

Contact info for Jonathan Pakianathan:
University of Rochester, Rochester NY 14620.

Contact info for Ergun Yalcin:
Bilkent University, Ankara, Turkey.

Paper Status: Will appear in Topology, vol 42/5 pg 1155-1183.

Abstract: In this paper we find upper bounds for the nilpotency degree of 
some ideals in the cohomology ring of a group by studying fixed point free 
actions of the group on suitable spaces. The ideals we study are the 
kernels of restriction maps to certain collections of proper subgroups. We 
recover the Quillen-Venkov lemma and the Quillen F-injectivity theorem as 
corollaries and discuss some generalizations and further applications.

We then consider the essential cohomology conjecture and show that it is 
related to group actions on connected graphs. We discuss an obstruction to 
constructing a fixed point free action of a group on a connected graph 
with zero "k-invariant" and study the class related to this obstruction. 
It turns out that this class is a "universal essential class" for the 
group and controls many questions about the group's essential cohomology 
and transfers from proper subgroups.