The Isomorphism Problem for All Hyperbolic Groups
By Franccois Dahmani, Vincent Guirardel. 2010
102 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/810061e770a683ec8399f37b32160ae462f6e4fa
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In Applied Mathematics
- Gilbert Levitt
- Vincent Guirardel
- Denis V. Osin
- Ashot Minasyan
- Cornelia Drutu
- D. Groves
- G. Hruska
- Jason A. Behrstock
In Geometry and Topology
- Vincent Guirardel
- Gilbert Levitt
- Denis V. Osin
- Alessandro Sisto
- Michael Hull
- Ashot Minasyan
- D. Groves
- Franccois Dahmani
In Mathematical Physics
- Vincent Guirardel
- Gilbert Levitt
- Denis V. Osin
- Alessandro Sisto
- Michael Hull
- Franccois Dahmani
- Anthony Genevois
- Mark F. Hagen
Citations in the corpus
- Splittings and automorphisms of relatively hyperbolic groups (2012, background): “enerated subgroups, one may decide whether Out(G;H(t)) is infinite. Proof. We start with the first assertion. We first construct an algorithm that stops if and only if Out(G) is finite. By Theorem 8.1 of [DG11], one can compute a finite generating set of Out(G). Moreover, one can solve the word problem i”
- GROUPS ACTING ACYLINDRICALLY ON HYPERBOLIC SPACES (2017, background): “This yields an approximation of relatively hyperbolic groups by hyperbolic ones, which in turn allows the authors make use of the solution of the isomorphism problem for hyperbolic groups obtained in [23].”