Let be the connected sum of knots . It is known that the -character variety of the knot exterior of has a component of dimension 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 satisfies the vanishing identity if each does so.
Cite this article
Joan Porti, Seokbeom Yoon, The adjoint Reidemeister torsion for the connected sum of knots. Quantum Topol. 14 (2023), no. 3, pp. 407–428DOI 10.4171/QT/180