On Knots with trivial Alexander polynomial

Garoufalidis, Stavros; Teichner, Peter

J. Differential Geom., Tome 66 (2004) no. 3, p. 167-193 / Harvested from Project Euclid

Résumé

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.

Publié le : 2004-05-14
Classification:

@article{1099587731,
     author = {Garoufalidis, Stavros and Teichner, Peter},
     title = {On Knots with trivial Alexander polynomial},
     journal = {J. Differential Geom.},
     volume = {66},
     number = {3},
     year = {2004},
     pages = { 167-193},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1099587731}
}

Garoufalidis, Stavros; Teichner, Peter. On Knots with trivial Alexander polynomial. J. Differential Geom., Tome 66 (2004) no. 3, pp.  167-193. http://gdmltest.u-ga.fr/item/1099587731/