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

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.

The two parts of this work have been through different publishing processes. The main reason of this is that part 2, and only part 2, relies at the time of writing on unpublished material. The two parts are shown here in a single arXiv document, numbering has been chosen to match the published versions. 43 pages in total

References in corpus (3)

• The isomorphism problem for all hyperbolic groups
• Foliations for solving equations in groups: free, virtually free, and hyperbolic groups
• The Isomorphism Problem for Toral Relatively Hyperbolic Groups

Cited by in corpus (5)

• Relative hyperbolicity for automorphisms of free products
• Free-by-cyclic groups, automorphisms and actions on nearly canonical trees
• The conjugacy problem for UPG elements of $Out(F_n)$
• The Conjugacy Problem for $Out(F_3)$
• Reducing the conjugacy problem for relatively hyperbolic automorphisms to peripheral components