4 problems

For each $n$, let $\mathcal H_s(T_n)$ be a complex with Poincaré polynomial $\mathcal P_s(T_n)$ and differentials $d_N$. Let “smallest” mean minimal with respect to the properties…

For positive integers $m,n$, define the normalized reduced superpolynomial … When the limit exists, call $\mathcal P_s(T_n)=\lim_{m\to\infty}\mathcal P_s(T_{m,n})$ the stable super…

Let $T_{3,m}$ be a torus knot, and let $\mathcal P(T_{3,m})$ denote its reduced superpolynomial. For $m=3k+1$ or $m=3k+2$, define the three polynomials…

Let $K$ be a knot, and let $\overline{\mathit{KhR}}_N(q,t)$ denote the graded Poincaré polynomial of the $sl(N)$ Khovanov–Rozansky homology. A finite polynomial has only finitely m…