Advanced Search

We show a relationship between the non-acyclic Reidemeister torsion and a zero of the acyclic Reidemeister torsion for a $\lambda$-regular $\mathrm{SU}\left(2\right)$ or $\mathrm{SL}(2,ℂ)$-representation of a knot group. Then we give a method to calculate the non-acyclic Reidemeister torsion of a knot exterior. We calculate a new example and investigate the behavior of the non-acyclic Reidemeister torsion associated to a $2$-bridge knot and $\mathrm{SU}\left(2\right)$-representations of its knot group.