On Knots with trivial Alexander polynomial
Geometric Topology
2007-05-23 v3 Quantum Algebra
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.
Cite
@article{arxiv.math/0206023,
title = {On Knots with trivial Alexander polynomial},
author = {Stavros Garoufalidis and Peter Teichner},
journal= {arXiv preprint arXiv:math/0206023},
year = {2007}
}
Comments
LaTeX, 15 pages with 23 figures