Homological representations of low genus mapping class groups
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909135809806336 |
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| author | Lucas, Trent |
| author_facet | Lucas, Trent |
| contents | Given a finite group $G$ acting on a surface $S$, the centralizer of G in the mapping class group $\textrm{Mod}(S)$ has a natural representation given by its action on the homology $H_1(S; \mathbb{Q})$. We consider the question of whether this representation has arithmetic image. Several authors have given positive and negative answers to this question. We give a complete answer when S has genus at most 3. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_03552 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Homological representations of low genus mapping class groups Lucas, Trent Geometric Topology Group Theory Representation Theory Given a finite group $G$ acting on a surface $S$, the centralizer of G in the mapping class group $\textrm{Mod}(S)$ has a natural representation given by its action on the homology $H_1(S; \mathbb{Q})$. We consider the question of whether this representation has arithmetic image. Several authors have given positive and negative answers to this question. We give a complete answer when S has genus at most 3. |
| title | Homological representations of low genus mapping class groups |
| topic | Geometric Topology Group Theory Representation Theory |
| url | https://arxiv.org/abs/2303.03552 |