Taking the High-Edge Route Through Outer Space in Rank 3

Abstract

Principal fully irreducible outer automorphisms were introduced in [AKKP19] to emulate principal pseudo-Anosov surface homeomorphisms, i.e. those whose attracting and repelling invariant foliations have only 3-pronged singularities. It is proved in [AKKP19] that these outer automorphisms semi-mimic principal pseudo-Anosov surface homeomorphisms in important ways. We prove here which rank-3 graphs carry train track representatives for principal fully irreducible outer automorphisms. As a corollary, one obtains which simplices of rank-3 Culler-Vogtmann Outer space are passed through by principal axes.