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May 2004 On Knots with trivial Alexander polynomial
Stavros Garoufalidis, Peter Teichner
J. Differential Geom. 67(1): 167-193 (May 2004). DOI: 10.4310/jdg/1099587731

Abstract

We use the 2-loop term of the Kontsevich integral to show that there are (many) knots with trivial Alexander polynomial which do not 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.

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Stavros Garoufalidis. Peter Teichner. "On Knots with trivial Alexander polynomial." J. Differential Geom. 67 (1) 167 - 193, May 2004. https://doi.org/10.4310/jdg/1099587731

Information

Published: May 2004
First available in Project Euclid: 4 November 2004

zbMATH: 1095.57007
MathSciNet: MR2153483
Digital Object Identifier: 10.4310/jdg/1099587731

Rights: Copyright © 2004 Lehigh University

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Vol.67 • No. 1 • May 2004
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