Rigidity of Fibonacci representations of mapping class groups
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909677762117632 |
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| author | Godfard, Pierre |
| author_facet | Godfard, Pierre |
| contents | We prove that level $5$ Witten-Reshetikhin-Turaev $\mathrm{SO}(3)$ quantum representations, also known as the Fibonacci representations, of mapping class groups are locally rigid. More generally, for any prime level $\ell$, we prove that the level $\ell$ $\mathrm{SO}(3)$ quantum representations are locally rigid on all surfaces of genus $g\geq 3$ if and only if they are locally rigid on surfaces of genus $3$ with at most $3$ boundary components. This reduces local rigidity in prime level $\ell$ to a finite number of cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_15366 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Rigidity of Fibonacci representations of mapping class groups Godfard, Pierre Geometric Topology Representation Theory We prove that level $5$ Witten-Reshetikhin-Turaev $\mathrm{SO}(3)$ quantum representations, also known as the Fibonacci representations, of mapping class groups are locally rigid. More generally, for any prime level $\ell$, we prove that the level $\ell$ $\mathrm{SO}(3)$ quantum representations are locally rigid on all surfaces of genus $g\geq 3$ if and only if they are locally rigid on surfaces of genus $3$ with at most $3$ boundary components. This reduces local rigidity in prime level $\ell$ to a finite number of cases. |
| title | Rigidity of Fibonacci representations of mapping class groups |
| topic | Geometric Topology Representation Theory |
| url | https://arxiv.org/abs/2303.15366 |