7 problems

Casson–Gordon's conjecture. Every 2-bridge ribbon knot is contained in one of the three families of Casson and Gordon.

Lamm's conjecture. $c_t(K)=c(K)$ if and only if $K$ can be represented by a continued fraction expansion $[a_1,\ldots,a_n]$ of type (A) or type (B).

Two-bridge knot transvergent diagram conjecture. A two-bridge knot $K$ has a transvergent diagram with $c(K)$ crossings if and only if one of these two conditions is fulfilled.

Dunfield's conjecture. For every rational slope $r\in I$, Dehn filling $K$ along slope $r$ is orderable.

Let $K$ be a two-bridge knot, and let $\Phi_K(2,y)$ be its Riley polynomial specialized at meridian trace $2$. The knot signature is denoted by $\sigma(K)$. Riley's conjecture. The…

Let … be the Alexander polynomial of a two-bridge knot. Convex-concave conjecture. There exists an integer $k\leq n$ such that $(a_0,\ldots,a_k)$ is convex and $(a_k,\ldots,a_n)$ i…

Let $K$ be a knot, and let $\pi_1(S^3\smallsetminus K)$ denote its knot group. Suppose this group is generated by two conjugate elements. Reid's conjecture. The elements are periph…