Residual finiteness, QCERF and fillings of hyperbolic groups

2008/02/29 by Ian Agol, Daniel Groves, Jason Fox Manning · 1 citation
Computer Science · Mathematics · #Geometric and Algebraic Topology #Geometry #Group (periodic table) #Homotopy and Cohomology in Algebraic Topology #Hyperbolic 3-manifold #Hyperbolic function #Hyperbolic group #Hyperbolic manifold #Hyperbolic triangle #Mathematical analysis #Mathematics #Pure mathematics #Regular polygon #Relatively hyperbolic group #Residual #Separable space #math.GR #math.GT #msc:20E26 #msc:20F65 #msc:20F67 #semigroups and automata theory

paper · pdf · doi:10.2140/gt.2009.13.1043

published as Geom. Topol. 13 (2009) 1043-1073 · (v1) 22 pages, 2 figures. (v2) 24 pages, 2 figures. An error in the proof and statement of the main technical lemma was corrected, and some other small corrections and clarifications were made

arxiv created 2008/03/10 · openalex publication_date 2009/01/21 · arxiv updated 2014/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We prove that if every hyperbolic group is residually finite, then every quasi-convex subgroup of every hyperbolic group is separable. The main tool is relatively hyperbolic Dehn filling.

Citations

• On Quasiconvexity and Relative Hyperbolic Structures
• Relatively Hyperbolic Groups
• Peripheral fillings of relatively hyperbolic groups
• Dehn filling in relatively hyperbolic groups
• Metric Spaces of Non-Positive Curvature
• Hyperbolic Groups

Cited by

• Separability of double cosets and conjugacy classes in 3-manifold groups
• Quasi-hyperbolic planes in relatively hyperbolic groups