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The Isomorphism Problem for All Hyperbolic Groups

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Abstract

We give a solution to Dehn’s isomorphism problem for the class of all hyperbolic groups, possibly with torsion. We also prove a relative version for groups with peripheral structures. As a corollary, we give a uniform solution to Whitehead’s problem asking whether two tuples of elements of a hyperbolic group G are in the same orbit under the action of Aut(G). We also get an algorithm computing a generating set of the group of automorphisms of a hyperbolic group preserving a peripheral structure.

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  1. François Dahmani

    Present address: Institut Fourier, Université de Grenoble I, 100 rue des maths, BP 74, F-38402, St. Martin d’Hères Cedex, France

  2. Vincent Guirardel

    Present address: Institut de Recherche en Mathématiques de Rennes (IRMAR), Université de Rennes 1, 263 avenue du Général Leclerc, CS 74205, F-35042, Rennes Cedex, France

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  1. Institut de Mathématiques de Toulouse, Université Paul Sabatier, Toulouse III, 118 route de Narbonne, F-31062, Toulouse Cedex 9, France

    François Dahmani & Vincent Guirardel

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  1. François Dahmani
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Correspondence to François Dahmani.

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Dahmani, F., Guirardel, V. The Isomorphism Problem for All Hyperbolic Groups. Geom. Funct. Anal. 21, 223–300 (2011). https://doi.org/10.1007/s00039-011-0120-0

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