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arXiv · 1307.2108

On suspensions, and conjugacy of hyperbolic automorphisms (and of a few more)

François Dahmani
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Abstract

Part 1 : We remark that the conjugacy problem for pairs of hyperbolic au- tomorphisms of a finitely presented group (typically a free group) is decidable. The solution that we propose uses the isomorphism problem for the suspensions, and the study of their automorphism group. Part 2 : In a previous work (part 1), we remarked that the conjugacy problem for pairs of atoroidal automorphisms of a free group was solvable by mean of the isomorphism problem for hyperbolic groups and an orbit problem for the automorphism group of their suspensions (i.e. their semidirect product with Z for the relevant structural automorphism). We consider the same problem a few more automorphisms of free groups, those that produce relatively hyperbolic suspensions that do not split over a parabolic subgroup.

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François Dahmani. 2013-07-08. On suspensions, and conjugacy of hyperbolic automorphisms (and of a few more). https://doi.org/10.1090/tran/6530

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