On Knots with trivial Alexander polynomial

Stavros Garoufalidis; Peter Teichner

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On Knots with trivial Alexander polynomial

Stavros Garoufalidis·Peter Teichner

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Abstract

We use the 2-loop term of the Kontsevich integral to show that there are (many) knots with trivial Alexander polynomial which don't have a Seifert surface whose genus equals the rank of the Seifert form. This is one of the first applications of the Kontsevich integral to intrinsically 3-dimensional questions in topology. Our examples contradict a lemma of Mike Freedman, and we explain what went wrong in his argument and why the mistake is irrelevant for topological knot concordance. References updated.

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BibTeX RIS

Stavros Garoufalidis, Peter Teichner. 2003-10-14. On Knots with trivial Alexander polynomial. https://arxiv.org/abs/math/0206023

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