On reciprocality of twisted Alexander invariants

Abstract

Given a knot and an ${SL}_n\mathbb{F}$ representation of its group that is conjugate to its dual, the representation that replaces each matrix with its inverse-transpose, the associated twisted Reidemeister torsion is reciprocal. An example is given of a knot group and ${SL}_3\mathbb{Z}$ representation for which the twisted Reidemeister torsion is not reciprocal.