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Contact homology and higher dimensional closing lemmas

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arxiv 2206.04738 v2 pith:B7IPF25P submitted 2022-06-09 math.SG math.DS

Julian Chaidez , Ipsita Datta , Rohil Prasad , Shira Tanny This is my paper · ORCID
classification math.SGmath.DS
keywords closingflowsreebcontacthomologylemmamethodsalbers-geiges-zehmisch
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We develop methods for studying the smooth closing lemma for Reeb flows in any dimension using contact homology. As an application, we prove a conjecture of Irie, stating that the strong closing lemma holds for Reeb flows on ellipsoids. Our methods also apply to other Reeb flows, and we illustrate this for a class of examples introduced by Albers-Geiges-Zehmisch.

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  1. 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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