Nilpotence in Group Cohomology

TL;DR

This paper investigates bounds on nilpotence in the mod p cohomology of classifying spaces of compact Lie groups, updating previous results with recent advances and providing new bounds for finite p-groups based on their subgroup structure.

Contribution

It updates earlier work on nilpotence bounds in group cohomology by incorporating recent verification of the Regularity Conjecture and introduces new bounds for finite p-groups.

Findings

Bounds on nilpotence in H*(BG) are established.

New results relate nilpotence bounds to subgroup structures of finite p-groups.

The work reflects recent developments in the field, including Symonds' verification of the Regularity Conjecture.

Abstract

We study bounds on nilpotence in H*(BG), the mod p cohomology of the classifying space of a compact Lie group G. Part of this is a report of our previous work on this problem, updated to reflect the consequences of Peter Symonds recent verification of Dave Benson's Regularity Conjecture. New results are given for finite p--groups, leading to good bounds on nilpotence in H*(BP) determined by the subgroup structure of the p--group P.