3 problems

Let $S^{2n+1}$ denote the $(2n+1)$-dimensional sphere, and let a contact manifold mean a manifold equipped with a contact structure. Sphere overtwistedness conjecture. The sphere…

Etnyre–Ng conjecture. $\Gamma_{-1,1}$ is the only non-loose Legendrian unknot that can be found in any overtwisted contact structure on $S^3$; equivalently, every non-loose Legendr…

Non-loose realization conjecture. If the hat Legendrian invariant of a Legendrian realization is non-zero, then the construction produces a non-loose realization in an overtwisted…