On Quasiconvexity and Relative Hyperbolic Structures

2008/11/14 by Eduardo Martínez-Pedroza, Eduardo Martinez-Pedroza, Martinez-Pedroza, Eduardo
Mathematics · #20F65 20F67 #Analytic and geometric function theory #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR #msc:20F65 #msc:20F67

paper · pdf · doi:10.48550/arxiv.0811.2384

Version to appear in Geometriae Dedicata. Included version of Bounded Coset Penetration for general relatively hyperbolic groups, two figures, and updated references

openalex publication_date 2008/11/14 · arxiv created 2011/05/02 · arxiv updated 2011/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a group which is hyperbolic relative to a collection of subgroups A, and it is also hyperbolic relative to a collection of subgroups B. Suppose that the collection A contains B. We characterize, for subgroups of G, when quasicovexity relative to A implies quasiconvexity relative to B. We also show that quasiconvexity relative to B implies quasiconvexity relative to A. Some applications are discussed.

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