Nilpotence in Group Cohomology

2010/02/24 by Nicholas J. Kuhn, Kuhn, Nicholas J.
Mathematics · #20J06 #55R40 #Algebraic Topology (math.AT) #FOS: Mathematics #Group Theory (math.GR) #math.AT #math.GR #msc:20J06 #msc:55R40

paper · pdf · doi:10.48550/arxiv.1002.4662

22 pages, better organized invariant theory results in section 4. Final version is in Proc. E.M.S. 56 (2013)

arxiv created 2013/06/25 · arxiv updated 2013/06/27

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.

Related

• Cohomology of p-groups of nil potency class smaller than p
• Cohomology of finite p-groups of fixed nilpotency class
• Homotopy nilpotency in p-compact groups
• Cohomology, fusion and a p-nilpotency criterion
• Testing Benson's Regularity Conjecture