Free group automorphisms with many fixed points at infinity

TL;DR

This paper constructs a family of free group automorphisms with a maximal number of fixed points at infinity, answering a question about the possible number of such fixed points.

Contribution

It introduces explicit automorphisms of free groups with many fixed points at infinity, demonstrating the maximal possible number as per recent theoretical bounds.

Findings

Automorphisms are irreducible with irreducible powers.

They have trivial fixed subgroup.

They possess 2n-1 attractive and 2n repelling fixed points at the boundary.

Abstract

A concrete family of automorphisms alpha_n of the free group F_n is exhibited, for any n > 2, and the following properties are proved: alpha_n is irreducible with irreducible powers, has trivial fixed subgroup, and has 2n-1 attractive as well as 2n repelling fixed points at bdry F_n. As a consequence of a recent result of V Guirardel there can not be more fixed points on bdry F_n, so that this family provides the answer to a question posed by G Levitt.