arXiv subjects

Linan Zhong

Publications and source records attributed to Linan Zhong.

3 recordsLinked to original sources

arXiv2024

Cohomology of $BPU_n$ and rings of invariants of Weyl groups

Let $PU_n$ denote the projective unitary group of rank $n$ and $BPU_n$ be its classifying space, for $n>1$. Using the Serre spectral sequence associated to the fibration $BU_n\to BPU_n\to K(\mathbb{Z},3)$, we compute the integral cohomology group of $BPU_n$ in dimensions $\leq 14$. In addition, we determine the ring structure of $H^*(BPU_n;\mathbb{Z})$ up to dimension $13$ by computing the ring of invariants $H^*(BT_{PU_n})^W$ of the Weyl group action in dimensions $\leq 12$.

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arXiv2024

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

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 $H^s(BPU_n;\mathbb{Z})_{(p)}$ for $s<2p+9$ by showing that $p$-primary subgroups of $H^s(BPU_n;\mathbb{Z})$ is $\mathbb{Z}/p$ for $s=2p+5$ and are trivial for $s = 2p+7$ and $s = 2p+8$, where $p$ is an odd prime.

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arXiv2021

The $p$-primary subgroups of the cohomology of $BPU_n$ in dimensions less than $2p+5$

Let $PU_n$ the projective unitary group of rank $n$ and $BPU_n$ its classifying space. For an odd prime $p$, we extend previous results to a compete 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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