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On number of ends of graph products of groups

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 Added by Olga Varghese
 Publication date 2019
  fields
and research's language is English
 Authors Olga Varghese




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Given a finite simplicial graph $Gamma=(V,E)$ with a vertex-labelling $varphi:Vrightarrowleft{text{non-trivial finitely generated groups}right}$, the graph product $G_Gamma$ is the free product of the vertex groups $varphi(v)$ with added relations that imply elements of adjacent vertex groups commute. For a quasi-isometric invariant $mathcal{P}$, we are interested in understanding under which combinatorial conditions on the graph $Gamma$ the graph product $G_Gamma$ has property $mathcal{P}$. In this article our emphasis is on number of ends of a graph product $G_Gamma$. In particular, we obtain a complete characterization of number of ends of a graph product of finitely generated groups.



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