5 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…

For each $n$, let $pc_{4n}$ be the degree $4n$ Vassiliev invariant constructed from Conway polynomial coefficients. Vassiliev-invariant strengthening. Each $pc_{4n}$ should be cong…

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 an amphicheiral knot, and let $\Delta_K$ be its Alexander polynomial. Stoimenow's sign conjecture. The sign of the leading coefficient of $\Delta_K$ is … The conjecture…

Let $K$ be an amphicheiral knot, and let $\Delta_K$ denote its Alexander polynomial; equivalently, consider the leading coefficient of its Conway polynomial. Stoimenow's square lea…