Random trees in the boundary of outer space

Kapovich, Ilya; Maher, Joseph; Pfaff, Catherine; Taylor, Selwyn

doi:10.2140/gt.2022.26.127

Geom. Topol.

2022

DOI: 10.2140/gt.2022.26.127

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Random trees in the boundary of outer space

Ilya Kapovich

Joseph Maher

Catherine Pfaff

et al.

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2023

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

Gagnier,

Pfaff

2023

Int. J. Algebra Comput.

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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.

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

Gagnier,

Pfaff

2023

Int. J. Algebra Comput.

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Random trees in the boundary of outer space

Cited by 1 publication

References 25 publications

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

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

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