Non injectivity of the "hair" map

Abstract

Kricker constructed a knot invariant Z^{rat} valued in a space of Feynman 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 from Vogel's zero divisor in the algebra Λ is in the kernel of H. This shows that H is not injective.

4 pages

References in corpus (2)

• A rational noncommutative invariant of boundary links
• The lines of the Kontsevich integral and Rozansky's rationality conjecture

Cited by in corpus (5)

• A universal equivariant finite type knot invariant defined from configuration space integrals
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• A surgery formula for the 2-loop piece of the LMO invariant of a pair
• On Knots with trivial Alexander polynomial
• Periodicity of Goussarov-Vassiliev knot invariants