Nontrivial Alexander polynomials of knots and links

Stefan Friedl; Stefano Vidussi

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arXiv · math/0606575

Nontrivial Alexander polynomials of knots and links

Stefan Friedl·Stefano Vidussi

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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.

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Stefan Friedl, Stefano Vidussi. 2007-01-24. Nontrivial Alexander polynomials of knots and links. https://arxiv.org/abs/math/0606575

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