3 problems

Periodic-representation detection conjecture. The knot $k$ is nonfibered if and only if there exist an integer $N>0$ and a periodic representation $\rho\in\Phi_{S_N}({\cal G})$ suc…

Let $k$ be a $2$-bridge knot, and let ${\gamma}_\phi$ be a total representation associated with a nonabelian parabolic representation ${\gamma}:\pi\to\operatorname{SL}_2\mathbb C$,…

Let $k$ be a knot with group $pi$, and for a representation ${\gamma}:\pi\to\operatorname{GL}_N\mathbb Z$, let $c_0$ and $c_1$ denote the trailing and leading coefficients, respect…