Polish Topologies for Graph Products of Cyclic Groups

2017/05/04 by Paolini, Gianluca, Shelah, Saharon
#03E15 #20B27 #20F65 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1705.01815

Abstract

We give a complete characterization of the graph products of cyclic groups admitting a Polish group topology, and show that they are all realizable as the group of automorphisms of a countable structure. In particular, we characterize the right-angled Coxeter groups (resp. Artin groups) admitting a Polish group topology. This generalizes results from [5], [7] and [4].

Related

• Polish Topologies for Graph Products of Groups
• The automorphism group of a graph product with no SIL
• Group Metrics for Graph Products of Cyclic Groups
• Some Results on Polish Groups
• Isomorphisms and automorphisms of graph products of groups