Quasi-isometries between groups with infinitely many ends

Abstract

Let G, F be finitely generated groups with infinitely many ends and let π1(Γ,A), π1(∆,B) be graph of groups decompositions of F, G such that all edge groups are finite and all vertex groups have at most one end. We show that G, F are quasi-isometric if and only if every one-ended vertex group of π1(Γ,A) is quasi-isometric to some one-ended vertex group of… (More)

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