8 problems

Volume duality conjecture. For every shrinkable link $L$,

Let $M$ be a $1$-cusped hyperbolic $3$-manifold, and let $M(p,q)$ denote the manifold obtained by $(p,q)$-Dehn filling on its cusp. Write $N_M(v)$ for the number of Dehn fillings o…

Let $M$ be an orientable hyperbolic 3-manifold with three cusps, and let $C_3$ denote the 3-chain link complement. Minimal-volume conjecture. The minimal volume of a 3-cusped orien…

Volume monotonicity conjecture.

Let $M$ be a hyperbolic $3$-manifold with positive first Betti number, so that $b_1(M)>0$. Minimum-volume conjecture. The smallest volume of such a manifold is $2v_3$, where $v_3$…

Non-orientable minimal limit volume conjecture. The minimal limit volume of non-orientable hyperbolic $3$-manifolds is $V_8$.

Asymptotic volume conjecture.

Minimal volume chain-link conjecture. For $n\leq 10$, the minimal-volume $n$-cusped orientable hyperbolic $3$-manifold is realized by a hyperbolic chain link that is minimally “twi…