On the p-primary subgroups of the cohomology of the classifying spaces of PUn
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917590030352384 |
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| author | Zhang, Zhilei Zhong, Linan |
| author_facet | Zhang, Zhilei Zhong, Linan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09103 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the p-primary subgroups of the cohomology of the classifying spaces of PUn Zhang, Zhilei Zhong, Linan Algebraic Topology 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. |
| title | On the p-primary subgroups of the cohomology of the classifying spaces of PUn |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2402.09103 |