Geodesic
Noninjectivity of the “hair” map
Patureau-Mirand, Bertrand1
1LMAM, Université de Bretagne-Sud, Université Européenne de Bretagne, BP 573, 56017 Vannes, France
Algebraic and Geometric Topology, Tome 12 (2012) no. 1, pp. 415-420
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Kricker constructed a knot invariant Zrat valued in a space of Feynman diagrams with beads. When composed with the “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 nontrivial element constructed from Vogel’s zero divisor in the algebra Λ is in the kernel of H. This shows that H is not injective.

DOI : 10.2140/agt.2012.12.415
Classification : 57M25, 57M27
Keywords: finite type invariant, Feynman diagram

Patureau-Mirand, Bertrand  1

1 LMAM, Université de Bretagne-Sud, Université Européenne de Bretagne, BP 573, 56017 Vannes, France 
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Patureau-Mirand, Bertrand. Noninjectivity of the “hair” map. Algebraic and Geometric Topology, Tome 12 (2012) no. 1, pp. 415-420. doi: 10.2140/agt.2012.12.415

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