Rigidity of $\mathbf{SU(2)}$ and $\mathbf{SO(3)}$ quantum representations of mapping class groups at prime levels
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912727564288000 |
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| author | Godfard, Pierre |
| author_facet | Godfard, Pierre |
| contents | We prove the rigidity of Witten-Reshetikhin-Turaev $\mathrm{SU}(2)$ and $\mathrm{SO}(3)$ quantum representations of mapping class groups at all prime levels for closed surfaces of genus at least $7$. The proof relies on Ocneanu rigidity of modular categories and harmonic representatives in Hodge theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19795 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rigidity of $\mathbf{SU(2)}$ and $\mathbf{SO(3)}$ quantum representations of mapping class groups at prime levels Godfard, Pierre Geometric Topology Algebraic Geometry Quantum Algebra 18M20, 14H10 (Primary) 57R56, 20G42 (Secondary) We prove the rigidity of Witten-Reshetikhin-Turaev $\mathrm{SU}(2)$ and $\mathrm{SO}(3)$ quantum representations of mapping class groups at all prime levels for closed surfaces of genus at least $7$. The proof relies on Ocneanu rigidity of modular categories and harmonic representatives in Hodge theory. |
| title | Rigidity of $\mathbf{SU(2)}$ and $\mathbf{SO(3)}$ quantum representations of mapping class groups at prime levels |
| topic | Geometric Topology Algebraic Geometry Quantum Algebra 18M20, 14H10 (Primary) 57R56, 20G42 (Secondary) |
| url | https://arxiv.org/abs/2511.19795 |