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The Giroux correspondence in arbitrary dimensions

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arxiv 2307.02317 v2 pith:P2Y5LHBE submitted 2023-07-05 math.SG

Joseph Breen , Ko Honda , Yang Huang This is my paper · ORCID
classification math.SG
keywords weinsteinlefschetzarbitrarycorrespondencedimensionsdomainfibrationgiroux
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We establish the Giroux correspondence in arbitrary dimensions. As corollaries we (i) give an alternate proof of a result of Giroux-Pardon that states that any Weinstein domain is Weinstein homotopic to one which admits a Weinstein Lefschetz fibration and (ii) prove that any two Weinstein Lefschetz fibrations whose Weinstein domain structures are Weinstein homotopic are related by the Weinstein Lefschetz fibration moves, affirming a conjecture of Giroux-Pardon.

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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. Convex hypersurfaces and robust heterodimensional dynamics

    math.SG 2026-07 accept novelty 7.0 of 10

    Any closed orientable hypersurface in a contact manifold of dimension ≥5 is isotopic via a C^{0}-small isotopy to a C^{2}-robustly non-convex hypersurface.

  2. Handle decompositions and stabilizations of open books

    math.GT 2025-05 conditional novelty 6.0 of 10

    A handle-exchange construction produces new open book decompositions in all dimensions n≥3 and shows every trivial-monodromy open book stabilizes to a page made of trivial disk bundles over spheres.

  3. Conformally symplectic topology from a dynamical viewpoint

    math.SG 2026-07 accept novelty 4.0 of 10

    Characteristic foliations of contact Hamiltonian manifolds determine convexity of hypersurfaces, with Morse-Smale implying convexity, C0-density of convex hypersurfaces, and C2-robust non-convex examples in dimensions ≥5.

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