Twisted Kuperberg invariants of knots and Reidemeister torsion via twisted Drinfeld doubles (Q6571605)

The main theorem of the paper (Theorem 4.2) is that an evaluation of the Reshetikhin-Turaev invariant of a knot in the three-sphere twisted by a representation of the fundamental group recovers the ``Fox-calculus twisted'' Kuperberg invariant in an earlier paper of the author [Algebr. Geom. Topol. 22, No. 5, 2419--2466 (2022; Zbl 1509.57009)]. As a consequence (Corollary 4.3) the paper gives a description of the \(SL(n,\mathbb{C})\)-twisted Reidemeister torsion of a knot complement as a Reshetikhin-Turaev invariant.