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2010 On the Kontsevich integral for knotted trivalent graphs
Zsuzsanna Dancso
Algebr. Geom. Topol. 10(3): 1317-1365 (2010). DOI: 10.2140/agt.2010.10.1317

Abstract

We construct an extension of the Kontsevich integral of knots to knotted trivalent graphs, which commutes with orientation switches, edge deletions, edge unzips and connected sums. In 1997 Murakami and Ohtsuki [Comm. Math. Phys. 188 (1997) 501–520] first constructed such an extension, building on Drinfel’d’s theory of associators. We construct a step-by-step definition, using elementary Kontsevich integral methods, to get a one-parameter family of corrections that all yield invariants well behaved under the graph operations above.

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Zsuzsanna Dancso. "On the Kontsevich integral for knotted trivalent graphs." Algebr. Geom. Topol. 10 (3) 1317 - 1365, 2010. https://doi.org/10.2140/agt.2010.10.1317

Information

Received: 27 November 2008; Revised: 30 January 2010; Accepted: 17 February 2010; Published: 2010
First available in Project Euclid: 19 December 2017

zbMATH: 1228.57002
MathSciNet: MR2661529
Digital Object Identifier: 10.2140/agt.2010.10.1317

Subjects:
Primary: 05C10, 57M15, 57M25, 57M27

Rights: Copyright © 2010 Mathematical Sciences Publishers

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Vol.10 • No. 3 • 2010
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