3 problems

Let $U$ be the standard Legendrian unknot, whose unique Reeb chord is denoted by $b$. A conical Legendrian filling $\Sigma$ of $U$ is equipped with a $1$-graded augmentation…

Let $n$ be a positive integer, and let $(S^{2n+1},\xi_\text{st})$ be the standard contact sphere. Let $\Lambda_0,\Lambda_1\subseteq(S^{2n+1},\xi_\text{st})$ be smooth Legendrian su…

Let $(X^{m+1},g)$, $m>1$, be a causally simple spacetime that does not admit a metric $g'$ such that $(X,g')$ is refocussing and causally simple. A Legendrian link is a link formed…