# The adjoint Reidemeister torsion for the connected sum of knots

### Joan Porti

Universitat Autònoma de Barcelona, Spain### Seokbeom Yoon

Universitat Autònoma de Barcelona, Spain

## Abstract

Let $K$ be the connected sum of knots $K_{1},…,K_{n}$. It is known that the $SL_{2}(C)$-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 $K_{i}$ 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. 407–428

DOI 10.4171/QT/180