In \cite{confol} Y. Eliashberg and W. Thurston gave a definition of tight confoliations. We give an example of a tight confoliation on violating the Thurston-Bennequin inequalities. This answers a question from \cite{confol} negatively. Although the tightness of a confoliation does not imply the Thurston-Benn…
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6 results for “confoliations”
Study confoliations' symplectic fillability, finding obstructions.
problem Understanding confoliations' symplectic fillability in higher dimensions.
method Generalized Massot-Niederkrüger-Wendl's bordered Legendrian open book for confoliations.
result Obstructions to weak symplectic fillability for confoliations.
Study how pairs of 1D foliations can be deformed into contact structures.
problem Understanding deformations of pairs of 1D foliations.
method Linear deformations of pairs of codimension one foliations into contact pairs.
result Main result provides applications and insights into foliation deformations.
We propose in this paper a method for studying contact structures in 3-manifolds by means of branched surfaces. We explain what it means for a contact structure to be carried by a branched surface embedded in a 3-manifold. To make the transition from contact structures to branched surfaces, we first define auxiliary ob…
Mitsumatsu constructed leafwise symplectic structures of certain codimension one foliations of the 5-sphere. This inspired the present author to improve his result on convergence of contact structure to foliation. We describe convergence of contact strcture to leafwise symplectic foliation by means of confoliation equi…
Let M be a closed oriented 3-manifold such that S^1 x M admits a symplectic structure w. The goal of this paper is to show that M is a fiber bundle over S^1. The basic idea is to use the obvious S^1-action on S^1 x M by rotating the first factor, and one of the key steps is to show that the S^1-action on S^1 x M is act…