Polish Topologies for Graph Products of Groups
Gianluca Paolini, Saharon Shelah
TL;DR
This paper establishes necessary conditions for when a graph product of groups can be endowed with a Polish group topology, providing a full characterization in the case where all factor groups are countable.
Contribution
It introduces strong necessary conditions for Polish topologies on graph products and offers a complete characterization for countable factor groups.
Findings
Necessary conditions for Polish topologies on graph products
Characterization modulo finite node sets
Complete characterization for countable factor groups
Abstract
We give strong necessary conditions on the admissibility of a Polish group topology for an arbitrary graph product of groups , and use them to give a characterization modulo a finite set of nodes. As a corollary, we give a complete characterization in case all the factor groups are countable.
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