Relative hyperbolicity for automorphisms of free products and free groups
| Autor: | Ruoyu Li, François Dahmani |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Computer Science::Information Retrieval 010102 general mathematics Astrophysics::Instrumentation and Methods for Astrophysics Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) Automorphism 01 natural sciences Mathematics::Group Theory Free product 0103 physical sciences Computer Science::General Literature 010307 mathematical physics Geometry and Topology 0101 mathematics Atoroidal Analysis Mathematics |
| Zdroj: | Journal of Topology and Analysis. 14:55-92 |
| ISSN: | 1793-7167 1793-5253 |
| DOI: | 10.1142/s1793525321500011 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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