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arXiv · 2001.05931

The mimimally displaced set of an irreducible automorphism of $F_N$ is co-compact

Stefano Francaviglia·Armando Martino·Dionysios Syrigos
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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 is consisted of a single point.

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Stefano Francaviglia, Armando Martino, Dionysios Syrigos. 2020-01-16. The mimimally displaced set of an irreducible automorphism of $F_N$ is co-compact. https://arxiv.org/abs/2001.05931

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