4 problems

Giroux-torsion vanishing conjecture. If

Let $T$ be a convex incompressible torus in a tight contact 3-manifold $(Y,\xi)$ such that every toric annulus neighborhood of $T$ with convex boundary is universally tight. Conjec…

No-torsion complement conjecture. The complement $Y\setminus B$ of the binding of an open book for any contact structure has no Giroux torsion. This is presented as a very weak for…

Let $(Y,\xi)$ be a contact 3-manifold. The binding number $bn(\xi)$ is the minimal number of binding components among open books supporting $\xi$ whose pages have minimal genus. Th…