2 problems

Suppose $K\subset S^3$ is a quasi-alternating knot. Let $\underline{\operatorname{KHI}}(-S^3,K)$ be the instanton knot Floer homology group, and let $d_+$ and $d_-$ be maps on it.…

Let a satellite knot be a knot whose exterior contains an incompressible torus. Let $\mathcal{Q}$ denote the class of quasi-alternating links, defined as the smallest set containin…