5 problems

Crosscap-three classification conjecture. For each even crossing number $2k\geq 6$, there are exactly

Let $L$ be a three-strand pretzel link $P(p,q,r)$, with folded ribbon realization $L_w$, and let ${\operatorname{Rib}}(L_w)$ denote its folded ribbonlength. Pretzel-link uniformity…

Let $R=Q(q^{\frac{1}{2}})$, let $L\subset S^3$ be a link with $n$ components, and let $E_L$ denote its exterior. For each component, let $t_i\in\mathcal{S}(E_L)$ be the meridian of…

Conjectural Type 3 braid-index formulas. In the first positive case, $\textbf{b}(\mathcal{L})=2+\sum\alpha_j$; in the second positive case, $\textbf{b}(\mathcal{L})=1+\sum\alpha_j$…

Let $L$ range over the $2$-component pretzel links that McCoy and McDonald proved are weakly doubly slice for all orientations but not strongly doubly slice. A link in $S^3$ is a b…