Groups quasi-isometric to H² x R

2000/05/25 by Eleanor G. Rieffel, Eleanor Rieffel, Rieffel, Eleanor G.
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Mathematics and Applications #math.GT

paper · pdf · doi:10.48550/arxiv.math/0005252

Journal of the London Math Society, to appear. Minor revisions and updated references. 19 pages

openalex publication_date 2000/05/25 · arxiv created 2000/08/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is a more succinct version of the author's 1993 UCLA mathematics thesis. It proves that any group quasi-isometric to the product of the hyperbolic plane with the real line is a finite extension of a cocompact lattice in either the isometry group of the product of the hyperbolic plane with the real line or the isometry group of the universal cover of SL(2,R).

Related

• Quasi-hyperbolic planes in hyperbolic groups
• Relatively hyperbolic groups with fixed peripherals
• Induced quasi-isometries of hyperbolic spaces, Markov chains, and acylindrical hyperbolicity
• Geometric rigidity of quasi-isometries in horospherical products
• Quasi-isometry rigidity of groups