Stavros Garoufalidis and Peter Teichner.
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.
Key words: Trivial Alexander polynomial, knots, Seifert surface, Kontsevich integral, concordance, slice, claspers.
Notes: 13 pages, 19 figures.