6 problems

Let $M\to S^2$ be a Seifert fibered rational homology sphere with fiber multiplicities $d_1,\dots,d_k$. Seifert H-cobordism conjecture. If $M$ is rationally H-cobordant to zero, th…

Nonfillability conjecture. No contact structure defined by Figure and satisfying conditions is fillable.

Distinctness conjecture. All the tight contact structures defined by Figure and satisfying the assumptions are distinct up to isotopy.

Generalized cabling conjecture. If Dehn surgery on $K$ yields a connected sum of more than $n-1$ lens spaces, then there is a Seifert fibering of $Y$ where $K$ is a regular fiber.

Three Fibers Conjecture. A Seifert fibered homology sphere with more than three singular fibers cannot bound a homology ball.

A Seifert fibered surgery is a Dehn surgery on a knot whose resulting $3$-manifold is Seifert fibered. The integrality conjecture. Any Seifert fibered surgery on a hyperbolic knot…