Random trees in the boundary of Outer space

Kapovich, Ilya; Maher, Joseph; Pfaff, Catherine; Taylor, Samuel J.

doi:10.48550/arxiv.1904.10026

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2020

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“…In [AKKP19], it is shown that the axes of principal fully irreducible outer automorphisms share a certain "stability" property with principal pseudo-Anosov axes in Teichmüller space. This stability property is then used in [KMPT18] and [KMPT19] to not only prove which outer automorphisms are random walk generic, but to understand properties held by a typical (with respect to the harmonic measure) tree in the boundary of Outer space.…”

Section: Introductionmentioning

confidence: 99%

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

Gagnier¹,

Pfaff²

2020

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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.

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Section: Introductionmentioning

confidence: 99%