The level $d$ mapping class group of a compact non-orientable surface
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909170980093952 |
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| author | Kobayashi, Ryoma |
| author_facet | Kobayashi, Ryoma |
| contents | Let $N_{g,n}$ be a genus $g$ compact non-orientable surface with $n$ boundaries. We explain about relations on the level $d$ mapping class group $\mathcal{M}_d(N_{g,0})$ of $N_{g,0}$ and the level $d$ principal congruence subgroup $Γ_d(g-1)$ of $\mathrm{SL}(g-1;\mathbb{Z})$. As applications, we give a normal generating set of $\mathcal{M}_d(N_{g,n})$ for $g\ge4$ and $n\ge0$, and finite generating sets of $\mathcal{M}_d(N_{g,n})$ for some $d$, any $g\ge4$ and $n\ge0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_13555 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The level $d$ mapping class group of a compact non-orientable surface Kobayashi, Ryoma Geometric Topology Let $N_{g,n}$ be a genus $g$ compact non-orientable surface with $n$ boundaries. We explain about relations on the level $d$ mapping class group $\mathcal{M}_d(N_{g,0})$ of $N_{g,0}$ and the level $d$ principal congruence subgroup $Γ_d(g-1)$ of $\mathrm{SL}(g-1;\mathbb{Z})$. As applications, we give a normal generating set of $\mathcal{M}_d(N_{g,n})$ for $g\ge4$ and $n\ge0$, and finite generating sets of $\mathcal{M}_d(N_{g,n})$ for some $d$, any $g\ge4$ and $n\ge0$. |
| title | The level $d$ mapping class group of a compact non-orientable surface |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2306.13555 |