Groups of proper homotopy equivalences of graphs and Nielsen Realization

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 co...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2021-09
Main Authors: Algom-Kfir, Yael, Bestvina, Mladen
Format: Article
Language:English
Subjects:
Equivalence
Isomorphism
Subgroups
Topology
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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 \(Y\).
ISSN:2331-8422