2004/01/31 by Francois Dahmani, FRANÇOIS DAHMANI
Mathematics · #Advanced Operator Algebra Research #Boundary (topology) #Class (philosophy) #Geometric and Algebraic Topology #Group (periodic table) #Hyperbolic group #Locally compact space #Mathematical Dynamics and Fractals #Relatively hyperbolic group #Sierpinski carpet #math.GR #msc:20F67
paper · pdf · doi:10.1142/s0218196705002530
published as Int. J. of Alg. and Comp., Vol. 15, Nos. 5-6 (2005) 893-906 · 10 pages. Added a precision on local connectedness for Lemma 2.3, thanks to B. Bowditch
openalex publication_date 2005/10/01 · arxiv created 2007/05/29 · openalex created_date 2016/06/24 · arxiv updated 2020/07/20 · openalex updated_date 2026/08/05
Given a class of compact spaces, we ask which groups can be maximal parabolic subgroups of a relatively hyperbolic group whose boundary is in the class. We investigate the class of one-dimensional connected boundaries. We get that any non-torsion infinite finitely-generated group is a maximal parabolic subgroup of some relatively hyperbolic group with connected one-dimensional boundary without global cut point. For boundaries homeomorphic to a Sierpinski carpet or a 2-sphere, the only maximal parabolic subgroups allowed are virtual surface groups (hyperbolic, or virtually ℤ + ℤ).