11 problems

Ishikawa--Shimokawa conjecture. Then

Ichihara's conjecture. For every knot $K$ in $S^3$,

Let $K$ be a hyperbolic knot in $S^3$ that admits non-trivial exceptional surgeries. A NIT boundary slope is a boundary slope that is non-integral or toroidal. For $b e{}$ an integ…

Let $K$ be a hyperbolic knot in $S^3$. A boundary slope is a slope represented by the boundary curves of an essential embedded surface in the exterior of $K$, and an exceptional su…

Kalfagianni–Tran's Strong Slope Conjecture. For any knot in $S^3$, every Jones slope satisfies $SS(n)$ for some $n\in\mathbb{N}$.

Garoufalidis's Slope Conjecture. For any knot $K$ in $S^3$, every Jones slope is a boundary slope:

Two slopes conjecture. If

Let $K$ be a knot, let $M_K$ be its exterior, and let $js_K$ be the set of Jones slopes obtained from the cluster points of $4n^{-2}d_+[J_K(n)]$. Let $jx_K$ be the cluster-point se…

HOMFLY slope conjecture. For any knot $K$,

Let $K$ be a prime non-torus knot and let $E(K)$ be its exterior. A properly embedded orientable incompressible and boundary incompressible surface in $E(K)$ may have a boundary sl…

Let $K$ be a 2-bridge knot, and suppose that its boundary-slope set has exactly four distinct elements. A 2-bridge knot $K_1$ is minimal with respect to the Silver–Whitten partial…