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Strongly adapted contact geometry of Anosov 3-flows

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arxiv 2410.21208 v3 pith:6QVTQN5D submitted 2024-10-28 math.SG math.DSmath.GT

Surena Hozoori This is my paper · ORCID
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We provide a 3 dimensional contact geometric characterization of Anosov 3-flows based on interactions with Reeb dynamics. We investigate basic properties of the space of the resulting geometries and in particular show that such space is homotopy equivalent to the space of Anosov 3-flows. A technical theorem on the asymptotic synchronization of adapted norms is proved, which can be of broader interest.

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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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