7 problems

Virtual Legendrian isotopy conjecture. Two Legendrian links in $ST^*S^m$ or $ST^*\mathbb C P^n$ are Legendrian isotopic if and only if they are virtually Legendrian isotopic. The s…

Strong virtual Legendrian unlinking conjecture. There is no non-negative strong allowable virtual Legendrian isotopy of one component of $L$ to the other.

Strong virtual Legendrian isotopy conjecture. There exists no strong allowable positive, or non-constant non-negative, virtual Legendrian isotopy of the sphere fiber of $ST^*M$ to…

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 $(X^{m+1},g)$ be a globally hyperbolic spacetime with $m\geq 2$. Two points are causally related when one lies in the causal future or causal past of the other, and their skies…

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…