Volume conjecture for closed three-manifolds

Let $M$ be a closed three-manifold. Write $\tau_N(M)$ for its $SU(2)$ Witten–Reshetikhin–Turaev invariant at level $N$, let $\operatorname{CS}(M)$ denote its Chern–Simons invariant, let $\Vert M\Vert$ be its simplicial volume, and define

$$\operatorname{Vol}(M):=v_3\Vert M\Vert.$$

Volume conjecture for closed three-manifolds.

$$\operatorname*{o\!\operatorname{-lim}}_{N\to\infty}\frac{2\pi\sqrt{-1}\log\tau_N(M)}{N}=\operatorname{CS}(M)+\sqrt{-1}\operatorname{Vol}(M).$$

The source calls this conjecture “very ambiguous”; it proposes a unified asymptotic relation between Witten–Reshetikhin–Turaev invariants, Chern–Simons invariants, and simplicial volume for closed three-manifolds.