On Knots with trivial Alexander polynomial

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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.
LaTeX, 15 pages with 23 figures

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Geometric Topology, Quantum Algebra

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http://salesiana.dossiersoluciones.com/handle/123456789/64216

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0206023
 http://arxiv.org/abs/math/0206023

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arXiv