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Dynamics of veering triangulations: infinitesimal components of their flow graphs and applications

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arxiv 2201.02706 v2 pith:3PJIHQOV submitted 2022-01-07 math.GT math.DS

Ian Agol , Chi Cheuk Tsang This is my paper · ORCID
classification math.GTmath.DS
keywords veeringcomponentstriangulationsapplicationsflowinfinitesimalprooftriangulation
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We study the strongly connected components of the flow graph associated to a veering triangulation, and show that the infinitesimal components must be of a certain form, which have to do with subsets of the triangulation which we call `walls'. We show two applications of this knowledge: (1) a fix of a proof in the original paper by the first author which introduced veering triangulations; and (2) an alternate proof that veering triangulations induce pseudo-Anosov flows without perfect fits, which was initially proved by Schleimer and Segerman.

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  1. A Sm\"org\aa sbord of (bi)contact structures, Reeb flows and pseudo-Anosov flows

    math.DS 2025-02 conditional novelty 5.0 of 10

    A rigidity theorem for bicontact geometry: a bitransverse Anosov Reeb flow forces the supporting Anosov flow to be skew and isotopically equivalent; the rest of the paper is an open-problem survey.

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