Cohomology of $BPU_n$ and rings of invariants of Weyl groups
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909660876898304 |
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| author | Fan, Feifei Zha, Jiaxi Zhang, Zhilei Zhong, Linan |
| author_facet | Fan, Feifei Zha, Jiaxi Zhang, Zhilei Zhong, Linan |
| contents | 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 $\leq 12$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16297 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cohomology of $BPU_n$ and rings of invariants of Weyl groups Fan, Feifei Zha, Jiaxi Zhang, Zhilei Zhong, Linan Algebraic Topology 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 $\leq 12$. |
| title | Cohomology of $BPU_n$ and rings of invariants of Weyl groups |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2407.16297 |