Classifying homeomorphism groups of infinite graphs
type: Item
instance of: scholarly article
title: Classifying homeomorphism groups of infinite graphs
zbMATH Open document ID: 1196.57035
author: Taras Banakh
author: K. Mine
author: K. Sakai
published in: Topology and its Applications
publication date: 2009-11-05T00:00:00Z
review text: To a graph \(\Gamma\) is associated a directed graph \(\overrightarrow{\Gamma}\). Let \(\Gamma^{(0)}\) denote the branch, end and isolated points of \(\Gamma\). Let \(\circ_\Gamma\), \(\kappa_\Gamma\) and \(\nu_\Gamma\) denote the respective cardinalities of the isolated circles of \(\Gamma\), the relatively compact components of \(\Gamma\setminus\Gamma^{(0)}\) and the remaining components of \(\Gamma\setminus\Gamma^{(0)}\). Let \(e_\Gamma=\kappa_\Gamma+\nu_\Gamma\aleph_0\). Endowing \(\mathcal H(\Gamma)\) and Aut\((\overrightarrow{\Gamma})\) with the compact-open topology, a homeomorphism \(\mathcal H(\Gamma)\to\text{Aut}(\overrightarrow{\Gamma})\times\Pi^{\circ_\Gamma}\mathbb T\times\Pi^{e_\Gamma}\l_2\) is exhibited and its effect on special subgroups is described. Similar results are given when the Whitney topology is used.
reviewed by: David B. Gauld
Mathematics Subject Classification ID: 57S05
Mathematics Subject Classification ID: 58D05
Mathematics Subject Classification ID: 46A13
Mathematics Subject Classification ID: 54H11
Mathematics Subject Classification ID: 57N17
Mathematics Subject Classification ID: 57N20
Mathematics Subject Classification ID: 22A05
Mathematics Subject Classification ID: 46T05
Mathematics Subject Classification ID: 46T10
Mathematics Subject Classification ID: 58D15
zbMATH DE Number: 5625482
zbMATH Keywords: homeomorphism group
zbMATH Keywords: Whitney topology
zbMATH Keywords: compact-open topology
zbMATH Keywords: identity component
zbMATH Keywords: orientation-preserving
zbMATH Keywords: PL homeomorphism
zbMATH Keywords: infinite graph
zbMATH Keywords: box product
zbMATH Keywords: small box product
MaRDI profile type: Publication
full work available at URL: j.topol.2009.08.020
OpenAlex ID: W1974671409
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DOI: 10.1016/J.TOPOL.2009.08.020
description: scientific article; zbMATH DE number 5625482