Birman-Hilden theory for big mapping class groups
Fuente:
arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866911376928145408 |
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| author | Colin, Nestor Hidalgo, Ruben Rolland, Rita Jiménez Morales, Israel Quispe, Saúl |
| author_facet | Colin, Nestor Hidalgo, Ruben Rolland, Rita Jiménez Morales, Israel Quispe, Saúl |
| contents | Let $S$ and $X$ be two connected topological surfaces without boundary, and assume that $S$ is either of infinite type or has negative Euler characteristic. In this paper, we prove that if $p:S\rightarrow X$ is a fully ramified branched covering map, then $p$ satisfies the Birman-Hilden property. This generalizes a theorem of Winarski, and the known results in the literature, to the context of surfaces of infinite type and branched covering maps of infinite degree. As an application, we show that the mapping class group (respectively, the braid group on $k$-strands) of a non-orientable surface of infinite type can be realized as a subgroup of the mapping class group (respectively, the braid group on $2k$-strands) of its orientable double cover. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09897 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Birman-Hilden theory for big mapping class groups Colin, Nestor Hidalgo, Ruben Rolland, Rita Jiménez Morales, Israel Quispe, Saúl Geometric Topology 57M12, 57K20 Let $S$ and $X$ be two connected topological surfaces without boundary, and assume that $S$ is either of infinite type or has negative Euler characteristic. In this paper, we prove that if $p:S\rightarrow X$ is a fully ramified branched covering map, then $p$ satisfies the Birman-Hilden property. This generalizes a theorem of Winarski, and the known results in the literature, to the context of surfaces of infinite type and branched covering maps of infinite degree. As an application, we show that the mapping class group (respectively, the braid group on $k$-strands) of a non-orientable surface of infinite type can be realized as a subgroup of the mapping class group (respectively, the braid group on $2k$-strands) of its orientable double cover. |
| title | Birman-Hilden theory for big mapping class groups |
| topic | Geometric Topology 57M12, 57K20 |
| url | https://arxiv.org/abs/2601.09897 |