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Abstract
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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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Keywords
Kontsevich integral, KTG, LMO invariant, associator
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Mathematical Subject Classification 2000
Primary: 05C10, 57M15, 57M25, 57M27
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Publication
Received: 27 November 2008
Revised: 30 January 2010
Accepted: 17 February 2010
Published: 11 June 2010
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