Research announcement: The structure of groups with a quasiconvex hierarchy

2009/10/01 by Daniel T. Wise · 3 citations
Mathematics · #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Homotopy and Cohomology in Algebraic Topology #Quasiconvex function #Mathematics #Hierarchy #Separable space #Group (periodic table) #Pure mathematics #Combinatorics #Regular polygon #Convex analysis #Mathematical analysis #Geometry #Convex optimization

paper · pdf · doi:10.3934/era.2009.16.44

openalex publication_date 2009/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

Let G be a word-hyperbolic group with a quasiconvex hierarchy.We show that G has a finite index subgroup G' that embeds as a quasiconvex subgroup of a right-angled Artin group.It follows that every quasiconvex subgroup of G is a virtual retract,and is hence separable.The results are applied to certain 3-manifold and one-relator groups.

Citations

• Subgroups of Surface Groups are Almost Geometric
• Dehn filling in relatively hyperbolic groups
• Codimension one subgroups and boundaries of hyperbolic groups

Cited by

• On some of the residual properties of finitely generated nilpotent\n groups
• 3-manifold [wikipedia]
• Virtually fibered conjecture [wikipedia]

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