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2012 Noninjectivity of the “hair” map
Bertrand Patureau-Mirand
Algebr. Geom. Topol. 12(1): 415-420 (2012). DOI: 10.2140/agt.2012.12.415

Abstract

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.

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Bertrand Patureau-Mirand. "Noninjectivity of the “hair” map." Algebr. Geom. Topol. 12 (1) 415 - 420, 2012. https://doi.org/10.2140/agt.2012.12.415

Information

Received: 9 December 2011; Accepted: 13 December 2011; Published: 2012
First available in Project Euclid: 19 December 2017

zbMATH: 1243.57008
MathSciNet: MR2916280
Digital Object Identifier: 10.2140/agt.2012.12.415

Subjects:
Primary: 57M25, 57M27

Rights: Copyright © 2012 Mathematical Sciences Publishers

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Vol.12 • No. 1 • 2012
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