6 problems

Let $K$ be a Montesinos knot with three branches. Here $M(0; (p,r),(q,s),(2mn\pm 1, 2n^2))$ denotes the Montesinos knot with the displayed parameters. Torisu's conjecture. The knot…

Let $\mathfrak{m}=\mathfrak{m}(a_1/b_1,a_2/b_2,\ldots,a_t/b_t)$ be a Montesinos knot with $t$ tangles. Consider its $\operatorname{PSL}_2(\mathbb C)$- and…

Montesinos rational unknotting conjecture. These three conditions are equivalent for all Montesinos knots.

A Montesinos knot is a knot in the Montesinos class, and a BB knot is a knot whose bridge index equals its braid index. The source refers to the non-alternating Montesinos knots de…

Let $M_0$ be a Montesinos knot, and let $K={\mathsf {cable}}(T_{m,n},M_0)$ be an $(m,n)$-cable of $M_0$. The bridge spectrum of $K$ is the Montesinos–pretzel bridge-spectrum conjec…

Torisu's conjecture. The knot satisfies $u(K)=1$ if and only if