12 problems

Let $K$ be a hyperbolic knot in $S^3$, and let $b[?25l\cT_Kb[?25h \in \C[t^{\pm1}]$ be its hyperbolic torsion polynomial. The Seifert genus of $K$ is denoted by $g(K)$. Hyperbolic…

Let $M$ be a $3$-manifold, let $\pi_1(M)_{r}^{(n)}$ denote the $n$th term of its rational derived series, and define … For each $n\in\mathbb{N}$, let $||\\,\cdot\\,||_n$ be the cor…

A-cone conjecture. For every natural number $k$, the set $\Gamma_k$ is an A-cone.

Let $M$ be a closed orientable irreducible atoroidal 3-manifold with positive first Betti number. An integral class is a class $a\in H^2(M;\mathbb{R})$ arising from integral cohomo…

Yazdi's virtual Euler class one conjecture. For any even integral lattice point $w\in H^2(M;{\mathbb R})$ of dual Thurston norm $1$, there exists some finite cover $\tilde{M}$ of…

Let $C(n,p)$ be the $n$-chained link with $p$ half-twists on its first component, and let $M(n,p)$ be its complement. For $p<0$, let $V(n,p)$ be a set of points in the Thurston uni…

Near-extremal intrinsic functional conjecture. There exists an $\epsilon>0$ such that

Open-book subsurface conjecture. $(Y,\xi)$ is tight if and only if every subsurface of the page of each supporting open book is Thurston norm minimizing and, moreover, has minimal…

General Milnor conjecture. If $\xi_L$ is tight, then $\Sigma$ maximizes Euler characteristic among all such surfaces.

Convexity question. Is the function $g$ convex?

Let $M$ and $N$ be admissible $3$-manifolds, and let $f\colon M\to N$ be a map that is surjective on $\pi_1(N)$ and induces isomorphisms … for every $n\geq 0$. For…

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…