Taking the high-edge route of rank-3 outer space

Abstract

Principal fully irreducible outer automorphisms were introduced in [Y. Algom-Kfir, I. Kapovich and C. Pfaff, Stable strata of geodesics in outer space, Int. Math. Res. Not. 2019(14) (2019) 4549–4578] 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 [Y. Algom-Kfir, I. Kapovich and C. Pfaff, Stable strata of geodesics in outer space, Int. Math. Res. Not. 2019(14) (2019) 4549–4578] 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 of principal fully irreducible outer automorphisms. As a corollary, one obtains which simplices of rank-3 Culler–Vogtmann outer space principal axes pass through.