Turaev–Viro invariants volume conjecture for compact orientable 3-manifolds

Let $M$ be a compact orientable $3$-manifold with empty or toroidal boundary. Let $TV_r(M,q)$ denote its $r$-th Turaev–Viro invariant, let $LTV(M)$ be the Turaev–Viro growth rate, let $v_3$ be the volume of a regular ideal hyperbolic tetrahedron, and let $||M||$ denote the simplicial volume of $M$. Here $r$ runs over all odd integers.

Turaev–Viro invariants volume conjecture. For every such $M$,

$$LTV(M)=\underset{r \xrightarrow{}\infty}{\operatorname{lim sup }}\frac{2\pi}{r}\operatorname{log}|TV_r(M,q)|=v_3||M||.$$

The conjecture is the generalized Turaev–Viro invariants volume conjecture for 3-manifolds, analogous to the volume conjecture for knots and hyperbolic 3-manifolds. The paper proves the equality for large families of Seifert fibered 3-manifolds, while the statement in this generality remains open.