Volume conjectures for the Reshetikhin-Turaev and the Turaev-Viro invariants

Qingtao Chen, Tian Yang

We consider the asymptotics of the Turaev-Viro and the Reshetikhin-Turaev invariants of a hyperbolic $3$-manifold, evaluated at the root of unity $\exp (2\pi \sqrt{-1}/r)$ instead…