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Elliptic associators and the LMO functor

Ronen Katsir

Science Faculty, School of Library Studies, The Hebrew University, The Edmond J. Safra Campus – Givat Ram, Jerusalem 9190401, Israel

E-mail Address: ronen.katz@mail.huji.ac.il

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https://doi.org/10.1142/S0218216516500024Cited by:1 (Source: Crossref)

Abstract

The elliptic associator of Enriquez can be used to define an invariant of tangles embedded in the thickened torus, which extends the Kontsevich integral. This construction by Humbert uses the formulation of categories with elliptic structures. In this work we show that an extension of the LMO functor also leads to an elliptic structure on the category of Jacobi diagrams which is used by the Kontsevich integral, and find the relation between the two structures. We use this relation to give an alternative proof for the properties of the elliptic associator of Enriquez. Those results can lead the way to finding associators for higher genera.

Keywords:

AMSC: 57M27, 57M25

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