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Article Dans Une Revue Journal of Topology and Analysis Année : 2022

Relative hyperbolicity for automorphisms of free products and free groups

Résumé

We prove that for a free product G with free factor system [Formula: see text], any automorphism [Formula: see text] preserving [Formula: see text], atoroidal (in a sense relative to [Formula: see text]) and none of whose power send two different conjugates of subgroups in [Formula: see text] on conjugates of themselves by the same element, gives rise to a semidirect product [Formula: see text] that is relatively hyperbolic with respect to suspensions of groups in [Formula: see text]. We recover a theorem of Gautero–Lustig and Ghosh that, if G is a free group, [Formula: see text] an automorphism of G, and [Formula: see text] is its family of polynomially growing subgroups, then the semidirect product by [Formula: see text] is relatively hyperbolic with respect to the suspensions of these subgroups. We apply the first result to the conjugacy problem for certain automorphisms (atoroidal and toral) of free products of abelian groups.

Dates et versions

hal-03951286 , version 1 (23-01-2023)

Identifiants

Citer

François Dahmani, Ruoyu Li. Relative hyperbolicity for automorphisms of free products and free groups. Journal of Topology and Analysis, 2022, 14 (01), pp.55-92. ⟨10.1142/S1793525321500011⟩. ⟨hal-03951286⟩
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