3 problems

Let $L$ be a Hopf link in $\mathbb{R}P^3$ whose components are colored by an $n$-dimensional skew-symmetric and/or $m$-dimensional symmetric representation $R$ of $su(2)$. Speciali…

Let $U$ be an unknot in $\mathbb{R}P^3$ colored by an $n$-dimensional skew-symmetric or symmetric representation $R$ of $su(2)$. Let $Z_{R\emptyset}(U;Q,q)$ be its invariant, and l…

In $\mathbb{R}P^3$, a knot is called class-$0$ if it has class $0$, and a knot is non-affine if it is not affine. Its genus is the minimum genus of a good surface bounding it. Exis…