Normalization of twisted Alexander invariants

Understand

Twisted Alexander invariants of knots are well-defined up to multiplication of units.

• We get rid of this multiplicative ambiguity via a combinatorial method and define normalized twisted Alexander invariants.
• We then show that the invariants coincide with sign-determined Reidemeister torsion in a normalized setting, and refine the duality theorem.
• We further obtain necessary conditions on the invariants for a knot to be fibered, and study behavior of the highest degrees of the invariants.