Bounding surface actions on hyperbolic spaces

2007/09/17 by Josh Barnard, Barnard, Josh
Mathematics · #20F65 #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR #math.GT #msc:20F65

paper · pdf · doi:10.48550/arxiv.0709.2722

v4: 8 pages; 3 figures; final version

openalex publication_date 2007/09/17 · arxiv created 2012/07/08 · arxiv updated 2012/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a diameter bound for fundamental domains for isometric actions of the fundamental group of a closed hyperbolic surface on a delta-hyperbolic space, where the bound depends on the hyperbolicity constant delta, the genus of the surface, and the injectivity radius of the action, which we assume to be strictly positive.

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