6 problems

Fix an even integer $n$, and consider the weaving knot $W(n+1,m)$, where $m$ is coprime to $n+1$. Along either of the two lines specified in Theorem 3, consider the normalized Khov…

Let $W(p,n)$ be a weaving knot, with $p$ and $n$ positive integers, and fix a crossing number. Largest-volume conjecture. The complements of weaving knots have the largest hyperbol…

Asymptotic twist-number conjecture. For $m$ sufficiently large,

Let the Jones polynomial of $W(3,n)$ have the form … For the coefficients indexed by $k$, write $\lambda_{-n+k}$ and $\lambda_{n-k}$ for the corresponding coefficients. Polynomial-…

Let $W(3,n)$ be a weaving knot, and write $T_k(W(3,n))$ for its $k$th twist number. Polynomial-degree conjecture. The function $T_k(W(3,n))$ is a polynomial in $n$ of degree $k$. T…

Let $W(3,n)$ denote the weaving knot of type $(3,n)$, and consider the ranks of its Khovanov homology as $n$ grows. Asymptotic normality conjecture. Asymptotically, the ranks of Kh…