Noninjectivity of the “hair” map

Patureau-Mirand, Bertrand

doi:10.2140/agt.2012.12.415

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Noninjectivity of the “hair” map

Bertrand Patureau-Mirand

Algebraic & Geometric Topology 12 (2012) 415–420

DOI: 10.2140/agt.2012.12.415

Abstract

Kricker constructed a knot invariant $Z^{rat}$ 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.

Keywords

finite type invariant, Feynman diagram

Mathematical Subject Classification 2010

Primary: 57M25, 57M27

References

Publication

Received: 9 December 2011

Accepted: 13 December 2011

Published: 14 March 2012

Authors

Bertrand Patureau-Mirand
LMAM Université de Bretagne-Sud Université Européenne de Bretagne BP 573 56017 Vannes France

Volume 12, issue 1 (2012)