The Chen-Yang volume conjecture for knots in handlebodies

In 2015, Chen-Yang proposed a volume conjecture using a family of Turaev-Viro type invariants for compact 3-manifolds. This is one of several volume conjectures that link quantum invariants of manifolds to the hyperbolic structure of these manifolds. This conjecture has since then been proved or numerically tested for several hyperbolic 3-manifolds, mostly for manifolds without boundary, but also manifolds with toroidal boundary and manifolds with totally geodesic boundary. However, there is currently no test of this conjecture for a hyperbolic 3-manifold with a boundary which has both a toroidal component and a totally geodesic boundary component. In this thesis, we thus propose to test the Chen-Yang hyperbolic volume conjecture for a family of 3-manifolds that can be seen as knot exteriors in a handlebody.