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

Zhilei Zhang; Linan Zhong

paper

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

arXiv:2402.09103

Abstract

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