Homomorphisms between pure mapping class groups
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914011951398912 |
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| author | de Pool, Rodrigo |
| author_facet | de Pool, Rodrigo |
| contents | Let $S$ and $S'$ be orientable finite-type surfaces of genus $g\geq 4$ and $g'$, respectively. We prove that every multitwist-preserving map between pure mapping class groups $\text{PMap}(S)\to \text{PMap}(S')$ is induced by a multi-embedding. As an application, we classify all homomorphisms $\text{PMap}(S)\to \text{PMap}(S')$ for $g\geq 4$ and $g' \leq 6\cdot 2^{g-4}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_18796 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Homomorphisms between pure mapping class groups de Pool, Rodrigo Geometric Topology Group Theory Let $S$ and $S'$ be orientable finite-type surfaces of genus $g\geq 4$ and $g'$, respectively. We prove that every multitwist-preserving map between pure mapping class groups $\text{PMap}(S)\to \text{PMap}(S')$ is induced by a multi-embedding. As an application, we classify all homomorphisms $\text{PMap}(S)\to \text{PMap}(S')$ for $g\geq 4$ and $g' \leq 6\cdot 2^{g-4}$. |
| title | Homomorphisms between pure mapping class groups |
| topic | Geometric Topology Group Theory |
| url | https://arxiv.org/abs/2410.18796 |