On the Kontsevich integral for knotted trivalent graphs

Dancso, Zsuzsanna

doi:10.2140/agt.2010.10.1317

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On the Kontsevich integral for knotted trivalent graphs

Zsuzsanna Dancso

Algebraic & Geometric Topology 10 (2010) 1317–1365

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.

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

Volume 10, issue 3 (2010)