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arXiv · 0705.2371

Normalization of twisted Alexander invariants

Takahiro Kitayama
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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.

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Takahiro Kitayama. 2015-07-05. Normalization of twisted Alexander invariants. https://arxiv.org/abs/0705.2371

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