Boundary convex cocompactness and stability of subgroups of finitely\n generated groups

2016/07/29 by Matthew Cordes, Cordes, Matthew, Matthew Gentry Durham +1
Mathematics · #20F65 #20F67 #20F69 #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Holomorphic and Operator Theory #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.1607.08899

openalex publication_date 2016/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A Kleinian group \Γ < \Isom( mathbb H³) is called convex\ncocompact if any orbit of \Γ in mathbb H³ is quasiconvex or,\nequivalently, \Γ acts cocompactly on the convex hull of its limit set in\n\∂ mathbb H³. Subgroup stability is a strong quasiconvexity condition\nin finitely generated groups which is intrinsic to the geometry of the ambient\ngroup and generalizes the classical quasiconvexity condition above.\nImportantly, it coincides with quasiconvexity in hyperbolic groups and convex\ncocompactness in mapping class groups. Using the Morse boundary, we develop an\nequivalent characterization of subgroup stability which generalizes the above\nboundary characterization from Kleinian groups.\n

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• Characterizations of Stability via Morse Limit Sets
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