English

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

Group Theory 2023-09-14 v4

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

R2 v1 2026-06-23T20:36:18.897Z