English

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.

Keywords

Cite

@article{arxiv.0705.2371,
  title  = {Normalization of twisted Alexander invariants},
  author = {Takahiro Kitayama},
  journal= {arXiv preprint arXiv:0705.2371},
  year   = {2015}
}
R2 v1 2026-06-21T08:28:57.094Z