Year: 2024
Type: preprint
Abstract: In this paper, we study confoliations in dimensions higher than three, mostly from the perspective of symplectic fillability. Our main result is that Massot-Niederkrüger-Wendl's bordered Legendrian open book, an object that obstructs the weak symplectic fillability of contact manifolds, admits a generalization for confoliations equipped with symplectic data. Applications include the non-fillability of the product of an overtwisted contact manifold and a class of symplectic manifolds, and the fact that Bourgeois contact structures associated with overtwisted contact manifolds admit no weak symplectic fillings for which the symplectic structure restricts at the boundary to a positive generator of the second cohomology of the torus factor. In addition, along the lines of the original 3-dimensional work of Eliashberg and Thurston, we give a new definition of approximation and deformation of confoliations by contact structures and describe some natural examples.
Authors: Cardona, Robert, Gironella, Fabio
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1190173965, Singular Symplectic Foliations in Contact, Symplectic and Poisson topology, Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation, New challenges in contact and symplectic topology, G4274939422, G464105488, G6325762137, G6910422418, G7013227978, G84477964
OpenAlex ID: W4403345583