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arXiv · 2011.14913

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

Damara Gagnier·Catherine Pfaff
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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.

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Damara Gagnier, Catherine Pfaff. 2020-11-30. Taking the High-Edge Route Through Outer Space in Rank 3. https://arxiv.org/abs/2011.14913

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