Turaev-Viro invariants and cabling operations

Abstract

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 preserved under (p, q)-cabling.