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Oriented Birkhoff sections of Anosov flows

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arxiv 2212.06483 v2 pith:2SJBCCDO submitted 2022-12-13 math.DS

Masayuki Asaoka , Christian Bonatti , Théo Marty This is my paper · ORCID
classification math.DS
keywords anosovbirkhofffactfloworientedauthorscovereddifferent
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abstract

This paper gives 3 different proofs (independently obtained by the 3 authors) of the following fact: given an Anosov flow on an oriented 3 manifold, the existence of a positive Birkhoff section is equivalent to the fact that the flow is $\mathbb{R}$-covered positively twisted.

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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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