We give strong necessary conditions on the admissibility of a Polish group topology for an arbitrary graph product of groups G(Γ,Ga), 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 Ga are countable.
Polish topologies for graph products of groups
Paolini, Gianluca;
2019-01-01
Abstract
We give strong necessary conditions on the admissibility of a Polish group topology for an arbitrary graph product of groups G(Γ,Ga), 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 Ga are countable.
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