Accidental parabolics and relatively hyperbolic groups

Abstract

By constructing, in the relative case, objects analoguous to Rips and Sela's canonical representatives, we prove that the set of images by morphisms without accidental parabolic, of a finitely presented group in a relatively hyperbolic group, is finite, up to conjugacy.

Revision, 24 pages, 4 figures

References in corpus (2)

• Combination of convergence groups
• Symbolic dynamics and relatively hyperbolic groups

Cited by in corpus (11)

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• Aspherical manifolds, relative hyperbolicity, simplicial volume and assembly maps
• Limits of (certain) CAT(0) groups, II: The Hopf property and the shortening argument
• Endomorphisms of relatively hyperbolic groups
• Proper actions on ${\ell }^p$ spaces for relatively hyperbolic groups
• Groups acting on tree-graded spaces and splittings of relatively hyperbolic group
• Bounding surface actions on hyperbolic spaces
• Straight thin combings