Nontrivial Alexander polynomials of knots and links

Details Nontrivial Alexander polynomials of knots and links Nontrivial Alexander polynomials of knots and links

2006-06-23

arxiv.org/abs/math/0606575v2

Mathematics

Geometric Topology

9 pages

Scientific paper

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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