Lone Axes in Outer Space

Abstract

Handel and Mosher define the axis bundle for a fully irreducible outer automorphism in "Axes in Outer Space." In this paper we give a necessary and sufficient condition for the axis bundle to consist of a unique periodic fold line. As a consequence, we give a setting, and means for identifying in this setting, when two elements of an outer automorphism group $Out(F_r)$ have conjugate powers.

Significant revisions for the sake of readability, several arguments filled in

References in corpus (2)

• Algorithmic detectability of iwip automorphisms
• A train track directed random walk on $Out(F_r)$

Cited by in corpus (5)

• Normalizers and centralizers of cyclic subgroups generated by lone axis fully irreducible outer automorphisms
• Random trees in the boundary of Outer space
• Counting conjugacy classes of fully irreducibles: double exponential growth
• Taking the High-Edge Route Through Outer Space in Rank 3
• Ideal Whitehead Graphs in $Out(F_r)$ IV: Building ideal Whitehead graphs in higher ranks and ideal Whitehead graphs with cut vertices