English

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.

Keywords

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}
}

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9 pages