Cohomology of character stacks via TQFTs
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910506185392128 |
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| author | Vogel, Jesse |
| author_facet | Vogel, Jesse |
| contents | We study the cohomology of $G$-representation varieties and $G$-character stacks by means of a topological quantum field theory (TQFT). This TQFT is constructed as the composite of a so-called field theory and the 6-functor formalism of sheaves on topological stacks. We apply this framework to compute the cohomology of various $G$-representation varieties and $G$-character stacks of closed surfaces for $G = \text{SU}(2), \text{SO}(3)$ and $\text{U}(2)$. This work can be seen as a categorification of earlier work, in which such a TQFT was constructed on the level of Grothendieck groups to compute the corresponding Euler characteristics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19857 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cohomology of character stacks via TQFTs Vogel, Jesse Algebraic Geometry Algebraic Topology 14M35, 22-08, 55N30, 57R56 We study the cohomology of $G$-representation varieties and $G$-character stacks by means of a topological quantum field theory (TQFT). This TQFT is constructed as the composite of a so-called field theory and the 6-functor formalism of sheaves on topological stacks. We apply this framework to compute the cohomology of various $G$-representation varieties and $G$-character stacks of closed surfaces for $G = \text{SU}(2), \text{SO}(3)$ and $\text{U}(2)$. This work can be seen as a categorification of earlier work, in which such a TQFT was constructed on the level of Grothendieck groups to compute the corresponding Euler characteristics. |
| title | Cohomology of character stacks via TQFTs |
| topic | Algebraic Geometry Algebraic Topology 14M35, 22-08, 55N30, 57R56 |
| url | https://arxiv.org/abs/2406.19857 |