Groups of proper homotopy equivalences of graphs and Nielsen Realization
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866929208978046976 |
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| author | Algom-Kfir, Yael Bestvina, Mladen |
| author_facet | Algom-Kfir, Yael Bestvina, Mladen |
| contents | For a locally finite connected graph $X$ we consider the group $Maps(X)$ of proper homotopy equivalences of $X$. We show that it has a natural Polish group topology, and we propose these groups as an analog of big mapping class groups. We prove the Nielsen Realization theorem: if $H$ is a compact subgroup of $Maps(X)$ then $X$ is proper homotopy equivalent to a graph $Y$ so that $H$ is realized by simplicial isomorphisms of $Y$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_06908 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Groups of proper homotopy equivalences of graphs and Nielsen Realization Algom-Kfir, Yael Bestvina, Mladen Geometric Topology 20E36, 20B27 For a locally finite connected graph $X$ we consider the group $Maps(X)$ of proper homotopy equivalences of $X$. We show that it has a natural Polish group topology, and we propose these groups as an analog of big mapping class groups. We prove the Nielsen Realization theorem: if $H$ is a compact subgroup of $Maps(X)$ then $X$ is proper homotopy equivalent to a graph $Y$ so that $H$ is realized by simplicial isomorphisms of $Y$. |
| title | Groups of proper homotopy equivalences of graphs and Nielsen Realization |
| topic | Geometric Topology 20E36, 20B27 |
| url | https://arxiv.org/abs/2109.06908 |