Taking the High-Edge Route Through Outer Space in Rank 3
Abstract
Principal outer automorphisms were introduced in Algom-Kfir-Kapovich-Pfaff 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 Algom-Kfir-Kapovich-Pfaff that principal fully irreducible outer automorphisms semi-mimic principal pseudo-Anosov surface homeomorphisms in important ways. We prove here which rank-3 graphs carry train track maps for principal fully irreducible outer automorphisms. As a corollary, one obtains which rank-3 Culler-Vogtmann Outer space simplices are passed through by principal axes.
Keywords
Cite
@article{arxiv.2011.14913,
title = {Taking the High-Edge Route Through Outer Space in Rank 3},
author = {Damara Gagnier and Catherine Pfaff},
journal= {arXiv preprint arXiv:2011.14913},
year = {2023}
}
Comments
Version for publication in International Journal of Algebra and Computation. Correction of figures and link to full automata