On the Kontsevich integral for knotted trivalent graphs

Details On the Kontsevich integral for knotted trivalent graphs On the Kontsevich integral for knotted trivalent graphs

2008-11-27

arxiv.org/abs/0811.4615v3

Algebraic and Geometric Topology 10 (2010) 1317--1365

Mathematics

Geometric Topology

Journal version, 47 pages

Scientific paper

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 [MO] 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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