  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.
