The adjoint Reidemeister torsion for the connected sum of knots

Let K be the connected sum of knots K1​,…,Kn​. It is known that the SL2​(C)-character variety of the knot exterior of K has a component of dimension ≥2 as the connected sum admits a so-called bending. We show that there is a natural way to define the adjoint Reidemeister torsion for such a high-dimensional component and prove that it is locally constant on a subset of the character variety where the trace of a meridian is constant. We also prove that the adjoint Reidemeister torsion of K satisfies the vanishing identity if each Ki​ does so.