Groups of proper homotopy equivalences of graphs and Nielsen Realization

Fuente: arXiv
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Main Authors: Algom-Kfir, Yael, Bestvina, Mladen
Format: Preprint
Published: 2021
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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