The minimally displaced set of an irreducible automorphism of F N is co-compact

Francaviglia, Stefano, Martino, Armando and Syrigos, Dionysios (2021) The minimally displaced set of an irreducible automorphism of F _N is co-compact. Archiv der Mathematik, 116 (4), 369-383. (doi:10.1007/s00013-021-01579-z).

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Abstract

We study the minimally displaced set of irreducible automorphisms of a free group. Our main result is the co-compactness of the minimally displaced set of an irreducible automorphism with exponential growth ϕ, under the action of the centraliser C(ϕ). As a corollary, we get that the same holds for the action of < ϕ> on Min(ϕ). Finally, we prove that the minimally displaced set of an irreducible automorphism of growth rate one consists of a single point.

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2001.05931v1 - Accepted Manuscript

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Submitted date: 16 January 2020

Accepted/In Press date: 8 January 2021

Published date: April 2021

Additional Information: Funding Information: This project has received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No 777822. The second and the third named authors acknowledge support from the Leverhulme Trust (RPG-2018-058 grant). Publisher Copyright: © 2021, The Author(s).

Keywords: 20E06, 20E36, 20E08, math.GR