Accidental parabolics and relatively hyperbolic groups
Copyright policy )Accidental parabolics and relatively hyperbolic groups
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
- Institut Fourier France
- Paul Sabatier University France
- Joseph Fourier University France
- French National Centre for Scientific Research France
- Grenoble Alpes University France
Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations, Generators, relations, and presentations of groups, Topological methods in group theory, relatively hyperbolic groups, Subgroup theorems; subgroup growth, morphisms without accidental parabolics, [MATH] Mathematics [math], Group Theory (math.GR), amalgamated free products, HNN extensions, Hyperbolic groups and nonpositively curved groups, Automorphisms of infinite groups, 20F65, 20E07, finitely presented groups, FOS: Mathematics, Geometric group theory, graphs of groups, Mathematics - Group Theory, [MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR], [MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]
Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations, Generators, relations, and presentations of groups, Topological methods in group theory, relatively hyperbolic groups, Subgroup theorems; subgroup growth, morphisms without accidental parabolics, [MATH] Mathematics [math], Group Theory (math.GR), amalgamated free products, HNN extensions, Hyperbolic groups and nonpositively curved groups, Automorphisms of infinite groups, 20F65, 20E07, finitely presented groups, FOS: Mathematics, Geometric group theory, graphs of groups, Mathematics - Group Theory, [MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR], [MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]
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