Combination of convergence groups

2002/03/31 by Francois Dahmani · 4 citations
Mathematics · #Advanced Operator Algebra Research #Boundary (topology) #Convergence (economics) #Geometric and Algebraic Topology #Group (periodic table) #Hyperbolic group #Hyperbolic manifold #Limit (mathematics) #Mathematical Dynamics and Fractals #Property (philosophy) #Relatively hyperbolic group #math.GR #msc:20E06 #msc:20F67

paper · pdf · doi:10.2140/gt.2003.7.933

published as Geom. Topol. 7 (2003) 933-963 · Published in Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper27.abs.html

openalex publication_date 2003/12/11 · arxiv created 2003/12/12 · arxiv updated 2014/11/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We state and prove a combination theorem for relatively hyperbolic groups seen as geometrically finite convergence groups. For that, we explain how to contruct a boundary for a group that is an acylindrical amalgamation of relatively hyperbolic groups over a fully quasi-convex subgroup. We apply our result to Sela's theory on limit groups and prove their relative hyperbolicity. We also get a proof of the Howson property for limit groups.

Citations

• Diophantine geometry over groups I : Makanin-Razborov diagrams
• A topological characterisation of relatively hyperbolic groups
• Relatively Hyperbolic Groups
• Acylindrical accessibility for groups
• Hyperbolic Groups

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