5 problems

General slice-Bennequin inequality. $(Y,\xi)$ is tight if and only if

Let $(M,\xi)$ be a contact 3-manifold. Let $X_\alpha$ be a Reeb vector field and $J$ a complex structure on the contact distribution, and let $\theta'$ denote the instantaneous rot…

Let $(M^3,\xi)$ be a closed contact manifold admitting a contact form $\alpha$ and a complex structure $J$ on $\xi$ such that … everywhere, where $X_\alpha$ is the Reeb field of…

A contact structure is tight if it contains no overtwisted disk, and the Thurston–Bennequin inequalities are the inequalities relating the Euler characteristic of a surface to its…

A contact structure on a simply connected complete Riemannian 3-manifold whose sectional curvature is 1/4-pinched is expected to be tight. The 1/4-pinched contact sphere conjecture…