Adjoint Reidemeister torsions of some 3-manifolds obtained by Dehn surgeries

Abstract

Abstract We determine the adjoint Reidemeister torsion of a $3$ -manifold obtained by some Dehn surgery along K, where K is either the figure-eight knot or the $5_2$ -knot. As in a vanishing conjecture (Benini et al. (2020, Journal of High Energy Physics 2020, 57), Gang et al. (2020, Journal of High Energy Physics 2020, 164), and Gang et al. (2021, Advances in Theoretical and Mathematical Physics 25, 1819–1845)), we consider a similar conjecture and show that the conjecture holds for the 3-manifold.