Volume 10, issue 3 (2010)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
On the Kontsevich integral for knotted trivalent graphs

Zsuzsanna Dancso

Algebraic & Geometric Topology 10 (2010) 1317–1365
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.

Keywords
Kontsevich integral, KTG, LMO invariant, associator
Mathematical Subject Classification 2000
Primary: 05C10, 57M15, 57M25, 57M27
References
Publication
Received: 27 November 2008
Revised: 30 January 2010
Accepted: 17 February 2010
Published: 11 June 2010
Authors
Zsuzsanna Dancso
Department of Mathematics
University of Toronto
40 Saint George Street, 6th floor
Toronto M5S 2E4
Canada
http://www.math.toronto.edu/zsuzsi