Bilipschitz versus quasi-isometric equivalence for higher rank lamplighter groups

2014/07/04 by Tullia Dymarz, Dymarz, Tullia, Irine Peng +3
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Metric Geometry (math.MG) #math.GR #math.MG

paper · pdf · doi:10.48550/arxiv.1407.1107

arxiv created 2014/07/04 · openalex publication_date 2014/07/04 · arxiv updated 2014/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe a family of finitely presented groups which are quasi-isometric but not bilipschitz equivalent. The first such examples were described by the first author and are the lamplighter groups F \wr ℤ where F is a finite group; these groups are finitely generated but not finitely presented. The examples presented in this paper are higher rank generalizations of these lamplighter groups and include groups that are of type F_n for any n.

Related

• Quasi-isometric rigidity for lamplighters with lamps of polynomial growth
• Asymptotic geometry of lamplighters over one-ended groups
• Sublinear Bilipschitz Equivalence and the Quasiisometric Classification of Solvable Lie Groups
• Pattern preserving quasi-isometries in lamplighter groups and other related groups
• Isoperimetric profiles of lamplighter-like groups