11 problems

Twisted Alexander polynomial detection conjecture. If, for every epimorphism $\alpha:\pi_1(N)\to G$ onto a finite group, $\Delta^{\alpha}_{N,\phi}$ is monic and

Regular-representation congruence. The twisted Alexander polynomial satisfies

Let $M$ be a cusped hyperbolic 3-manifold, let $\mathcal{T}$ be an ideal triangulation, and choose an epimorphism $\alpha:\pi_1(M)\twoheadrightarrow\mathbb{Z}$, equivalently an inf…

Let $K$ be a hyperbolic knot, let $g(K)$ denote its genus, and let $\rho_{\rm holo}:\pi(K)\to\operatorname{SL}(2,\mathbb{C})$ be a lift of the discrete and faithful representation…

Let $C$ be a curve whose components all intersect transversely, let $\rho$ range over the representations under consideration, and let $\Delta_1$ and $\Delta_0$ denote the twisted…

Let $K\subset S^3$ be a hyperbolic oriented knot, and let $\pi_K$ denote its knot group. Let $\alpha\colon \pi_K\to \operatorname{SL}(2,\mathbb{C})$ be a lift of the discrete and f…

Let $K$ be a knot and let … be a non-abelian linear representation, where $D_\ell$ is the dihedral group of order $2\ell$ and $\ell$ is an odd prime. Hirasawa–Murasugi conjecture.…

Hyperbolic torsion polynomial detection conjecture. The hyperbolic torsion polynomial $4\mathcal{T}_K4$ determines $x(K)$, or equivalently its genus. Moreover, $K$ is fibered if an…

Let $K$ be a knot with knot group $G(K)$, and suppose there is a homomorphism $f:G(K)\twoheadrightarrow M(n\mid p,k)$. Let $N=\langle s\rangle=\{1,s,s^2,\ldots,s^{n-1}\}$ and let…

Generalized evaluation conjecture.

Silver–Williams conjecture.