Conjugacy problem in groups of oriented geometrizable 3-manifolds |
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Authors: | Jean-Philippe Pré aux |
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Affiliation: | a Ecole de l’air, CREA, 13661 Salon de Provence air, France b Centre de Mathématiques et d’informatique, Université de Provence, 39 rue F.Joliot-Curie, 13453 marseille cedex 13, France |
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Abstract: | The aim of this paper is to show that the fundamental group of an oriented 3-manifold which satisfies Thurston's geometrization conjecture has a solvable conjugacy problem. In other words, for any such 3-manifold M, there exists an algorithm which can decide for any couple of elements u,v of π1(M) whether u and v are in the same conjugacy class of π1(M) or not. More topologically, the algorithm decides for any two loops in M, whether they are freely homotopic or not. |
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Keywords: | Conjugacy problem Fundamental group 3-manifold Thurston geometrization conjecture JSJ decomposition Seifert fibered space Hyperbolic 3-manifold Graph of group Fuchsian group Word-hyperbolic group Relatively hyperbolic group |
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