The minimally displaced set of an irreducible automorphism of $$F_N$$ is co-compact-Reference-Cited by-同舟云学术

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

Published:2021-03-09 Issue:4 Volume:116 Page:369-383
ISSN:0003-889X
Container-title:Archiv der Mathematik
language:en
Short-container-title:Arch. Math.

Author:

Francaviglia Stefano,Martino Armando,Syrigos Dionysios^ORCID

Abstract

AbstractWe 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

$$\phi $$

ϕ , under the action of the centraliser

$$C(\phi )$$

C ( ϕ ) . As a corollary, we get that the same holds for the action of

$$ <\phi>$$

< ϕ > on

$$Min(\phi )$$

M i n ( ϕ ) . Finally, we prove that the minimally displaced set of an irreducible automorphism of growth rate one consists of a single point.

Funder

Leverhulme Trust

H2020 Marie Skłodowska-Curie Actions

Publisher

Springer Science and Business Media LLC

Subject

General Mathematics

Link

https://link.springer.com/content/pdf/10.1007/s00013-021-01579-z.pdf

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