Turaev-Viro invariants and cabling operations

In this paper, we study the variation of the Turaev-Viro invariants for 3-manifolds with toroidal boundary under the operation of attaching a (p,q)-cable space. We apply our results to a conjecture of Chen and Yang which relates the asymptotics of the Turaev-Viro invariants to the simplicial volume of a compact oriented 3-manifold. For p and q coprime, we show that the Chen-Yang volume conjecture is stable under (p,q)-cabling. We achieve our results by studying the linear operator RTr associated to the torus knot cable spaces by the Reshetikhin-Turaev SO3-Topological Quantum Field Theory (TQFT), where the TQFT is well-known to be closely related to the desired Turaev-Viro invariants. In particular, our utilized method relies on the invertibility of the linear operator for which we provide necessary and sufficient conditions.