On $H^*(BPU_n; \mathbb{Z})$ and Weyl group invariants
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866912385621557248 |
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| author | Crowley, Diarmuid Gu, Xing |
| author_facet | Crowley, Diarmuid Gu, Xing |
| contents | For the projective unitary group $PU_n$ with a maximal torus $T_{PU_n}$ and Weyl group $W$, we show that the integral restriction homomorphism
\[ρ_{PU_n} \colon H^*(BPU_n;\mathbb{Z})\rightarrow H^*(BT_{PU_n};\mathbb{Z})^W\]
to the integral invariants of the Weyl group action is onto. We also present several rings naturally isomorphic to $H^*(BT_{PU_n};\mathbb{Z})^W$.
In addition we give general sufficient conditions for the restriction homomorphism $ρ_G$ to be onto for a connected compact Lie group $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_03523 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On $H^*(BPU_n; \mathbb{Z})$ and Weyl group invariants Crowley, Diarmuid Gu, Xing Algebraic Topology 55R35, 55R40, 55T10 For the projective unitary group $PU_n$ with a maximal torus $T_{PU_n}$ and Weyl group $W$, we show that the integral restriction homomorphism \[ρ_{PU_n} \colon H^*(BPU_n;\mathbb{Z})\rightarrow H^*(BT_{PU_n};\mathbb{Z})^W\] to the integral invariants of the Weyl group action is onto. We also present several rings naturally isomorphic to $H^*(BT_{PU_n};\mathbb{Z})^W$. In addition we give general sufficient conditions for the restriction homomorphism $ρ_G$ to be onto for a connected compact Lie group $G$. |
| title | On $H^*(BPU_n; \mathbb{Z})$ and Weyl group invariants |
| topic | Algebraic Topology 55R35, 55R40, 55T10 |
| url | https://arxiv.org/abs/2103.03523 |