6 problems

Let $K$ be an amphicheiral knot, and let $C_K(z)$ denote its Conway polynomial. Conant's integral splitting conjecture. For some $\phi\in\mathbb Z[z]$, one has … The conjecture str…

Let $K\subset S^3$ be an amphicheiral knot, and let $\nabla_K(z)\in\mathbb{Z}[z^2]$ be its Conway polynomial. Kawauchi's mod 4 conjecture. There is an $f\in\mathbb{Z}[z]$ such that…

Let $K$ be a smooth knot whose Conway polynomial has an odd quadratic term. An inscribed knot is a knot obtained from points on $K$ by connecting consecutive points with straight s…

Takemura’s conjecture. Their coefficients satisfy $a_i=b_i$ when $i\equiv 0,1\pmod 4$, and $a_i=-b_i$ when $i\equiv 2,3\pmod 4$. The paper records this as a conjecture without stat…

Alternating quadrisecant approximation conjecture. Such sequences exist for every $\varepsilon>0$. The conjecture would connect the existence of alternating quadrisecants with insc…

Conway coefficient sign conjecture. The conclusion of the two-component obstruction holds whenever $L\in\mathcal{P}_0$: in general, the sign $(-1)^k$ is replaced by $(-1)^{s(k,m)}$…