3 problems

Let $L(p,q)$ be a lens space, and consider tight contact structures on it obtained from $(S^3,\xi_{\mathrm{st}})$ by a single Legendrian surgery. The examples described in the surr…

Contact Berge conjecture. Legendrian surgery on a knot in the standard tight contact structure on $S^3$ should yield a lens space if and only if the knot is a Legendrian realizatio…

Let $\Lambda=\bigsqcup_{v\in\Gamma}\Lambda_v$ be a Legendrian submanifold, with $\Gamma=\Gamma^+\cup\Gamma^-$, and let $C_v$ denote the associated co-core disks. Write…