2016/09/03 by Yi Lin, Lin, Yi
Mathematics · #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.1609.00773
openalex publication_date 2016/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we develop symplectic Hodge theory on transversely symplectic foliations. In particular, we establish the symplectic dδ-lemma for any such foliations with the (transverse) s-Lefschetz property. As transversely symplectic foliations include many geometric structures, such as contact manifolds, co-symplectic manifolds, symplectic orbifolds, and symplectic quasi-folds as special examples, our work provides a unifying treatment of symplectic Hodge theory in these geometries. As an application, we show that on compact K-contact manifolds, the s-Lefschetz property implies a general result on the vanishing of cup products, and that the cup length of a 2n+1 dimensional compact K-contact manifold with the (transverse) s-Lefschetz property is at most 2n-s. For any even integer s≥ 2, we also apply our main result to produce examples of K-contact manifolds that are s-Lefschetz but not (s+1)-Lefschetz.