3 problems

For every knot $K\subset S^3$, let $F_K^N(x,q)=F_K^{\mathfrak{sl}_N,\mathrm{sym}}(x,q)$ denote the series associated with symmetric representations, let $\Delta_K(x)$ be the Alexan…

Let $K$ be a knot with corresponding quiver $Q_K$. For each crossing of type $L_+$, let $K_{i,\tau}$, with $\tau\binom{}{}$ replaced by $\tau eq$? be the knot or link obtained by ch…

Let $K$ be a knot, let $a$ and $q$ be parameters, and let $\hat{A}_K(\hat{x},\hat{y},a,q)$ be the $a$-deformed quantum $A$-polynomial. HOMFLY-PT analogue conjecture. There exists a…