Classifying homeomorphism groups of infinite graphs
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.
scientific article; zbMATH DE number 5625482
scientific article