Document Type
Preprint
Publication Date
12-14-2017
Publication Title
The Quarterly Journal of Mathematics
DOI
10.1093/qmath/hax051
ISSN
1464-3847
Abstract
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.
Recommended Citation
Lin, Yi.
2017.
"Hodge Theory on Transversely Symplectic Foliations."
The Quarterly Journal of Mathematics: 1-25.
doi: 10.1093/qmath/hax051
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/597
Comments
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