Groups of proper homotopy equivalences of graphs and Nielsen Realization

Yael Algom-Kfir; Mladen Bestvina

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arXiv · 2109.06908

Groups of proper homotopy equivalences of graphs and Nielsen Realization

Yael Algom-Kfir·Mladen Bestvina

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Abstract

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 $Y$.

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BibTeX RIS

Yael Algom-Kfir, Mladen Bestvina. 2021-09-14. Groups of proper homotopy equivalences of graphs and Nielsen Realization. https://arxiv.org/abs/2109.06908

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