Nontrivial Alexander polynomials of knots and links
Geometric Topology
2018-12-24 v2
Abstract
In this paper we present a sequence of link invariants, defined from twisted Alexander polynomials, and discuss their effectiveness in distinguish knots. In particular, we recast and extend by geometric means a recent result of Silver and Williams on the nontriviality of twisted Alexander polynomials for nontrivial knots. Furthermore building on results in [FV06b] we prove that these invariants decide if a genus one knot is fibered, and we also show that these invariants distinguish all mutants with up to 12 crossings.
Cite
@article{arxiv.math/0606575,
title = {Nontrivial Alexander polynomials of knots and links},
author = {Stefan Friedl and Stefano Vidussi},
journal= {arXiv preprint arXiv:math/0606575},
year = {2018}
}
Comments
9 pages