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Non injectivity of the "hair" map

Bertrand Patureau-Mirand
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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.

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BibTeXRIS

Bertrand Patureau-Mirand. 2011-12-13. Non injectivity of the "hair" map. https://doi.org/10.2140/agt.2012.12.415

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