Kricker constructed a knot invariant valued in a space of Feynman diagrams with beads. When composed with the “hair” map , it gives the Kontsevich integral of the knot. We introduce a new grading on diagrams with beads and use it to show that a nontrivial element constructed from Vogel’s zero divisor in the algebra is in the kernel of . This shows that is not injective.
"Noninjectivity of the “hair” map." Algebr. Geom. Topol. 12 (1) 415 - 420, 2012. https://doi.org/10.2140/agt.2012.12.415