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Classifying Spaces and Boundaries for Relatively Hyperbolic Groups
Author(s) -
Dahmani François
Publication year - 2003
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611502013989
Subject(s) - coset , mathematics , hyperbolic group , mathematics subject classification , bounded function , relatively hyperbolic group , pure mathematics , boundary (topology) , space (punctuation) , torsion (gastropod) , hyperbolic manifold , combinatorics , mathematical analysis , hyperbolic function , computer science , medicine , surgery , operating system
We prove the following: if a group Γ is torsion‐free, and relatively hyperbolic (with the Bounded Coset Penetration property), relative to a subgroup admitting a finite classifying space, then Γ admits a finite classifying space. In this case, if the subgroup admits a boundary in the sense of Z‐structures, we prove that Γ admits a boundary. This extends classical results of Rips, and of Bestvina and Mess to the relative case. 2000 Mathematics Subject Classification 20F67, 20F69.