2000/05/22 by Lee Mosher, Mosher, Lee, Michah Sageev +3
Computer Science · Mathematics · #(primary) 20F65 #(secondary) 20F69 #20E06 #20E08 #Advanced Graph Theory Research #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR #msc:20E06 #msc:20E08 #msc:20F65 #msc:20F69 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.math/0005210
19 pages
arxiv created 2000/05/22 · openalex publication_date 2000/05/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop a battery of tools for studying quasi-isometric rigidity and classification problems for splittings of groups. The techniques work best for finite graphs of groups where all edge and vertex groups are coarse PD groups. For example, if Gamma is a graph of coarse PD(n) groups for a fixed n, if the Bass-Serre tree of Gamma has infinitely many ends, and if H is a finitely generated group quasi-isometric to pi1(Gamma), then we prove that H is the fundamental group of a graph of coarse PD(n) groups, with vertex and edge groups quasi-isometric to those of Gamma. We also have quasi-isometric rigidity theorems for graphs of coarse PD groups of nonconstant dimension, under various assumptions on the edge-to-vertex group inclusions.