12 problems

Let $T(c)$ be the set of objects with crossing number $c$ considered in the paper, and let the variance of their signatures be computed with respect to the uniform distribution on…

Let $K=C(p,q)$ be a positive 2-bridge knot with rational number $p/q$, where $p,q>20$. Let $v_3$, $a_2$, $a_4$, $\det(K)$, and $g$ denote the knot invariants used in the obstructio…

Vernitski's conjecture. The knot semigroup of every 2-bridge knot is isomorphic to an alternating sum semigroup.

Sliceness conjecture for 2-bridge knots. For all $2$-bridge knots $K$, $g_{4}(K)=0$ if and only if $g_{4}^{{\rm top}}(K)=0$.

Let $K_{m^2,q}$ be a 2-bridge knot, and let $\mathcal{R}$ denote the family of ribbon knots. The Casson–Gordon signature invariants associated to the double branched cover are the…

Let $K$ be a 2-bridge knot, and let $M$ be the module defined in the source by the referenced construction. Let the nonsymmetric skein module of $K$ be regarded as a module over th…

Large-parameter stability conjecture. There exists a positive integer $N_m$ such that: if $m$ is even, then $K(r_m)$ is $c$-stable for $k\geq N_m$; and if $m$ is odd, then $K(r_m)$…

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…

Representation-polynomial divisibility conjecture. If $f_2(z)$ divides $f_1(z)$, then there exists an epimorphism

Generalized evaluation conjecture.

Silver–Williams conjecture.

Mod 4 characterization conjecture. $\mu(r)=-1$ if and only if $r$ is (mod 4)-equivalent to either $[p]$ or $[3p]$.