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Twisted Alexander polynomial and Reidemeister torsion. (English) Zbl 0863.57001
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

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.
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