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

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 $\varphi$, under the action of the centraliser $C(\varphi )$. As a corollary, we get that the same holds for the action of $<\varphi >$ on $Min(\varphi )$. Finally, we prove that the minimally displaced set of an irreducible automorphism of growth rate one is consisted of a single point.

12 pages

References in corpus (1)

• Convexity of balls in the outer space