5 problems

Homological detection conjecture. If

Przytycki's torsion conjecture. The following are equivalent:

Let $M$ be a submanifold of a rational homology sphere. Assume that $M$ contains no closed, oriented incompressible surface. Let ${\cal S}_3(M)$ denote its Homflypt skein module, l…

Let $L$ be a non-trivial, non-split link, and let $E(L)$ denote its exterior. A closed surface $F$ containing $L$ has each component of $L$ non-separating in $F$ when no component…

Let $K$ be a prime non-torus knot, let $F$ be a non-orientable spanning surface for $K$, and let $E(K)$ be the exterior of $K$. The surface $F\cap E(K)$ is required to be geometric…