Cohomology of the universal centralizers I: the adjoint group case
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929625215533056 |
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| author | Jin, Xin |
| author_facet | Jin, Xin |
| contents | We compute the rational cohomology of the universal centralizer $J_G$ (also known as the Toda system or BFM space) for a complex (connected) semisimple group $G$ of adjoint form. While $J_G$ exhibits interesting and increasingly complex topology as the rank of $G$ rises, its rational cohomology is surprisingly simple--it coincides with that of a point. In a subsequent work [Jin2], we will extend this analysis to the case of $J_G$ for general semisimple $G$. In particular, we will show that its rational cohomology has pure Hodge structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09041 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cohomology of the universal centralizers I: the adjoint group case Jin, Xin Representation Theory Algebraic Geometry Geometric Topology We compute the rational cohomology of the universal centralizer $J_G$ (also known as the Toda system or BFM space) for a complex (connected) semisimple group $G$ of adjoint form. While $J_G$ exhibits interesting and increasingly complex topology as the rank of $G$ rises, its rational cohomology is surprisingly simple--it coincides with that of a point. In a subsequent work [Jin2], we will extend this analysis to the case of $J_G$ for general semisimple $G$. In particular, we will show that its rational cohomology has pure Hodge structure. |
| title | Cohomology of the universal centralizers I: the adjoint group case |
| topic | Representation Theory Algebraic Geometry Geometric Topology |
| url | https://arxiv.org/abs/2411.09041 |