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Taut foliations and contact pairs in dimension three

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arxiv 2405.15635 v1 pith:7FFLPEOB submitted 2024-05-24 math.SG math.DSmath.GT

Thomas Massoni This is my paper · ORCID
classification math.SGmath.DSmath.GT
keywords foliationscontactpairstautconstructiondimensionpartresult
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abstract

We present a new construction of codimension-one foliations from pairs of contact structures in dimension three. This constitutes a converse result to a celebrated theorem of Eliashberg and Thurston on approximations of foliations by contact structures. Under suitable hypotheses on the initial contact pairs, the foliations we construct are taut, allowing us to characterize taut foliations entirely in terms of contact geometry. This viewpoint reveals some surprising flexible phenomena for taut foliations, and provides new insight into the $L$-space conjecture. The first part of the proof builds upon the work on Colin and Firmo on positive contact pairs. The second part involves a wide generalization of a technical result of Burago and Ivanov on the construction of branching foliations tangent to continuous plane fields, and might be of independent interest.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Pseudo-Anosov flows on hyperbolic L-spaces

    math.GT 2025-05 accept novelty 8.0 of 10

    For every even n≥4, infinitely many surgeries on the n-chain link are hyperbolic L-spaces with n orbit-inequivalent pseudo-Anosov flows and n universally tight non-contactomorphic contact structures.

  2. Infinite ECH Capacities and Anosov Flows

    math.SG 2026-06 unverdicted novelty 7.0 of 10

    ECH capacities are infinite for cotangent disk bundles over genus at least two surfaces, obstructing oriented Anosov Hamiltonian flows in dimension four.

  3. Topological invariance of Liouville structures for taut foliations and Anosov flows

    math.SG 2025-10 conditional novelty 7.0 of 10

    Topologically conjugate taut foliations and orbit-equivalent Anosov flows produce exact symplectomorphic Liouville thickenings; the smoothing method also yields new collapsed Anosov flows.

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