Normalization of twisted Alexander invariants

Abstract

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.

15 pages, 1 figure; corrected the error about displaying a figure; 18 pages, 1 figure, modified the normalization of invariants and added a certain theorem; 19 pages, 1 figure, improved Theorem 6.6; to appear in International Journal of Mathematics

Cited by in corpus (3)

• Poincaré duality and degrees of twisted Alexander polynomials
• Alexander-Lin twisted polynomials
• Twisted Alexander polynomials, symplectic 4-manifolds and surfaces of minimal complexity