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

Gu, Xing; Zhang, Yu; Zhang, Zhilei; Zhong, Linan

doi:10.1090/proc/16000

The $p$-primary subgroups of the cohomology of $BPU_n$ in dimensions less than $2p+5$
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by Xing Gu, Yu Zhang, Zhilei Zhang and Linan Zhong PDF

Proc. Amer. Math. Soc. 150 (2022), 4099-4111 Request permission

Abstract:

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

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