On the p-primary subgroups of the cohomology of the classifying spaces of PUn

2024/02/14 by Zhang, Zhilei, Zhong, Linan
#Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2402.09103

Abstract

Let PU_n denote the projective unitary group of rank n, and let BPU_n be its classifying space. We extend our previous results to a description of H^s(BPU_n;ℤ)_(p) for s<2p+9 by showing that p-primary subgroups of H^s(BPU_n;ℤ) is ℤ/p for s=2p+5 and are trivial for s = 2p+7 and s = 2p+8, where p is an odd prime.

Related

• The p-primary subgroups of the cohomology of BPU_n in dimensions less than 2p+5
• Operators on symmetric polynomials and applications in computing the cohomology of BPU_n
• The cohomology of the classifying space of PU(4)
• A formula for the mod p cohomology of BPU(p)
• Cohomology of BPU_n and rings of invariants of Weyl groups