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Skewed Anosov flows are orbit equivalent to Reeb-Anosov flows in dimension 3
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abstract
We prove that in dimension 3, Anosov flows which are $\mathbb{R}$-covered and skewed are orbit equivalent to Reeb-Anosov flows. We characterize the existence of an invariant contact form or of a Birkhoff section with a given boundary, in terms of linking numbers between two invariant signed measures. Furthermore, we prove the existence of open book decompositions with one boundary component for Reeb-Anosov flows.
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Cited by 2 Pith papers
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Partial section III: for Anosov flows
A homology criterion for partial cross-sections of Anosov flows is established along with a finiteness result, implying every Anosov flow on a 3-dimensional hyperbolic manifold is homologically full.
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A Sm\"org\aa sbord of (bi)contact structures, Reeb flows and pseudo-Anosov flows
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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