6 problems

Smallest-volume conjecture. The Whitehead link complement $S^3\setminus K(8,3)$ has the smallest volume among all two-bridge two-component link complements.

Non-$L$-space conjecture. For every integer $n>0$, the two-bridge link $b(6n+4,-3)$ is a non-$L$-space link, and its Alexander polynomial satisfies the constraints of Theorem.

Classification conjecture. The set of all $L$-space two-bridge links is

Trapezoidal conjecture. There exists $n\leq \lfloor m/2\rfloor$ such that

Let $\rho$ be a $\mathrm{PSL}(2,\mathbb{C})$-representation of \pi_1(\text{\boldmathT}), and let $\mathcal{E}(\rho)\subset\mathcal{PL}$ denote its set of end invariants. An acc…

Trapezoidal conjecture. There exists an integer $n\leq\lfloor m/2\rfloor$ such that