Quasi-isometric rigidity for PSL(2,Z[1/p])

1998/09/19 by Jennifer Taback, Taback, Jennifer
Mathematics · #20F32 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #math.GR #math.GT #msc:20F32

paper · pdf · doi:10.48550/arxiv.math/9809108

29 pages, 4 figures, LaTeX, epsfig

arxiv created 1998/09/19 · arxiv updated 2009/11/30

Abstract

We prove that PSL(2,Z[1/p]) gives the first example of groups which are not quasi-isometric to each other but have the same quasi-isometry group. Namely, PSL(2,Z[1/p]) and PSL(2,Z[1/q]) are not quasi-isometric unless p=q, and, independent of p, the quasi-isometry group of PSL(2,Z[1/p]) is PSL(2,Q). In addition, we characterize PSL(2,Z[1/p]) uniquely among all finitely generated groups by its quasi-isometry type.

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