Non injectivity of the "hair" map
Résumé
Kricker and Garoufalidis have constructed an invariant of knots Z^rat with values in a space of diagrams with beads. When composed with the so called ''hair'' map H, It gives the Kontsevich integral of the knot. We introduce a new grading on diagrams with beads and use it to show that a non trivial element constructed with Vogel's zero divisor in the algebra Lambda is in the kernel of H. This shows that H is not injective.