The 𝑝-primary subgroups of the cohomology of 𝐵𝑃𝑈_{𝑛} in dimensions less than 2𝑝+5

Abstract

Let P U n PU_n denote the projective unitary group of rank n n and B P U n BPU_n be its classifying space. For an odd prime p p , we extend previous results to a complete description of H s ( B P U n ; Z ) ( p ) H^s(BPU_n;\mathbb {Z})_{(p)} for s > 2 p + 5 s>2p+5 by showing that the p p -primary subgroups of H s ( B P U n ; Z ) H^s(BPU_n;\mathbb {Z}) are trivial for s = 2 p + 3 s = 2p+3 and s = 2 p + 4 s = 2p+4 .

Milnor operations and classifying spaces

“…Many mathematicians have studied it in various contexts. Antieau, Gu and Williams ([AW14], [Gu19], [Gu20], [GZZZ22]) studied it for the topological period-index problem. Antieau, the author and Tripathy ([Ant16], [Kam15], [Kam17], [Tri16]) studied it for integral Hodge conjecture modulo torsion.…”