Construction of Hodge structures on the $\mathrm{SO}(3)$ modular functors
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929256850784256 |
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| author | Godfard, Pierre |
| author_facet | Godfard, Pierre |
| contents | We prove that $\mathrm{SO}(3)$ modular functors in genus $0$ have geometric origin and support integral variations of Hodge structures for any odd level $r$ and $r$-th root of unity $ζ_r\in\mathbb{C}$. We identify the TQFT intersection forms and integral structures with the geometric ones. Moreover, the gluing property of the modular functors is recovered geometrically as a Künneth formula. The construction is based on the homological models of Felder-Wieczerkowski and Martel. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_16804 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Construction of Hodge structures on the $\mathrm{SO}(3)$ modular functors Godfard, Pierre Geometric Topology Algebraic Geometry Quantum Algebra 57R56, 14D07, 20G42 (Primary) 14H10, 32G15 (Secondary) We prove that $\mathrm{SO}(3)$ modular functors in genus $0$ have geometric origin and support integral variations of Hodge structures for any odd level $r$ and $r$-th root of unity $ζ_r\in\mathbb{C}$. We identify the TQFT intersection forms and integral structures with the geometric ones. Moreover, the gluing property of the modular functors is recovered geometrically as a Künneth formula. The construction is based on the homological models of Felder-Wieczerkowski and Martel. |
| title | Construction of Hodge structures on the $\mathrm{SO}(3)$ modular functors |
| topic | Geometric Topology Algebraic Geometry Quantum Algebra 57R56, 14D07, 20G42 (Primary) 14H10, 32G15 (Secondary) |
| url | https://arxiv.org/abs/2402.16804 |