10 problems

The ν–barmu conjecture. The $\nu$-invariant equals the $\bar\mu$-invariant for every Seifert fibered homology sphere $Y$:

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.

Let $M$ be a Seifert fibered homology $3$-sphere, and call the singular fibers of the Seifert fibration exceptional fibers. Lawson's three fibers conjecture. If $M$ has more than t…

Let $K$ be a hyperbolic knot, and call a surgery slope non-integer when its slope is not an integer. A Seifert fibered manifold is a 3-manifold admitting a Seifert fibration. Non-i…

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…

The $bar\mu$-invariant is an integral lift of the Rohlin invariant for plumbed homology $3$-spheres. Let $Y=\Sigma(a_1,\ldots,a_n)$ be a Seifert fibered homology sphere, and let…