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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.20242 |
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| _version_ | 1866910549921497088 |
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| author | Chandran, Yassin Cremaschi, Tommaso |
| author_facet | Chandran, Yassin Cremaschi, Tommaso |
| contents | In this work we show two results about approximating, with respect to the compact-open topology, mapping classes on surfaces of infinite-type by quasi-conformal maps, in particular we are interested in density results. The first result is that given any infinite-type surface $S$ there exists a hyperbolic structure $X$ on $S$ such that $\text{PMCG}(S)\subseteq \overline{\text{Mod}(X)}$, for $\text{Mod}(X)$ the set of quasi-conformal homeomorphism on $X$. The second result is that given any surface $S$ with countably many ends then there exists a hyperbolic structure $X$ such that $\text{MCG} (S)=\overline{\text{Mod}(X)}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_20242 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Density results for the modular group of infinite-type surfaces Chandran, Yassin Cremaschi, Tommaso Geometric Topology In this work we show two results about approximating, with respect to the compact-open topology, mapping classes on surfaces of infinite-type by quasi-conformal maps, in particular we are interested in density results. The first result is that given any infinite-type surface $S$ there exists a hyperbolic structure $X$ on $S$ such that $\text{PMCG}(S)\subseteq \overline{\text{Mod}(X)}$, for $\text{Mod}(X)$ the set of quasi-conformal homeomorphism on $X$. The second result is that given any surface $S$ with countably many ends then there exists a hyperbolic structure $X$ such that $\text{MCG} (S)=\overline{\text{Mod}(X)}$. |
| title | Density results for the modular group of infinite-type surfaces |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2403.20242 |