12 problems

Limsup volume conjecture. For every non-splittable link $L$,

Let $n$ be a positive integer, and let $\{\mathfrak{n},\ldots,1,0\}$ be a sequence. Link spectrum realization conjecture. Any sequence $\{\mathfrak{n},\ldots,1,0\}$ satisfying a se…

Asymptotic average genus conjecture.

Detcherry–Kalfagianni–Yang colored-Jones volume question.

Detcherry–Kalfagianni–Yang generalized Turaev–Viro volume conjecture.

Murakami–Murakami simplicial-volume conjecture.

Let $L$ be a link in a contact three-manifold $Y$, and let $\alpha$ be any contact form on $Y$ adapted to $L$. Denote by $ECK(L,Y,\alpha)$ and $\widehat{ECK}(L,Y,\alpha)$ the full…

Kauffman's conjecture. Every pseudo-alternating link is alternative.

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 $L$ be an amphicheiral link in $S^3$, meaning that an orientation-reversing homeomorphism of $S^3$ maps each component of $L$ to a component of $L$, possibly reversing orientat…

Let $L$ be a prime, nonsplit two-component link, and let $\Sigma(L)$ denote its intrinsic symmetry group. The link has full symmetry when $\Sigma(L)=\Gamma_2$, where $\Gamma_2$ is…

so(3) volume conjecture. For all knots and links $L$,