Kitano, Teruaki Twisted Alexander polynomial and Reidemeister torsion. (English) Zbl 0863.57001 Pac. J. Math. 174, No. 2, 431-442 (1996). In 1992, Wada defined the twisted Alexander polynomial for any finitely presentable group. We consider the case of a knot group. Then it is a generalization of the classical Alexander polynomial of a knot. Milnor investigated the connection between the Alexander polynomial of a knot and the Reidemeister torsion of an exterior of a knot in 1962. We consider the following problem, that is: Can we consider the twisted Alexander polynomial of a knot as a Reidemeister torsion of its exterior? In fact, the answer is yes. As an application of this interpretation, we obtain a proof that the twisted Alexander polynomial of a knot for an \(SO(n)\)-representation is symmetric. Reviewer: Teruaki Kitano Cited in 1 ReviewCited in 54 Documents MSC: 57M05 Fundamental group, presentations, free differential calculus 57M25 Knots and links in the \(3\)-sphere (MSC2010) 57Q10 Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc. Keywords:twisted Alexander polynomial; finitely presentable group; knot group; Reidemeister torsion PDFBibTeX XMLCite \textit{T. Kitano}, Pac. J. Math. 174, No. 2, 431--442 (1996; Zbl 0863.57001) Full Text: DOI