Normalization of twisted Alexander invariants
Geometric Topology
2015-07-07 v5
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.
Cite
@article{arxiv.0705.2371,
title = {Normalization of twisted Alexander invariants},
author = {Takahiro Kitayama},
journal= {arXiv preprint arXiv:0705.2371},
year = {2015}
}