Elliptic associators and the LMO functor (Q2788555)
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scientific article; zbMATH DE number 6543067
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Elliptic associators and the LMO functor |
scientific article; zbMATH DE number 6543067 |
Statements
Elliptic associators and the LMO functor (English)
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19 February 2016
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elliptic associators
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tangle invariants
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LMO functor
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cobordisms
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Jacobi diagrams
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0.8814679
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0.8774987
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0.8710634
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0.86948997
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0.86619204
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The paper under review compares two constructions for LMO invariants of a tangle in a thickened torus. First, \textit{P. Humbert}'s construction which uses an elliptic associator [Intégrale de Kontsevich elliptique et enchevêtrements en genre supérieur. Université de Strasbourg, PhD Thesis (2012), \url{http://www.theses.fr/2012STRAD042}]. Second, a construction based on the LMO functor which uses a Drinfel'd associator [\textit{D. Cheptea} et al., Geom. Topol. 12, No. 2, 1091--1170 (2008; Zbl 1148.57017)]. The two LMO invariants are shown to be equal modulo a certain ``homotopy'' relation. This equivalence is used to provide a new proof for the properties of the elliptic associator of \textit{B. Enriquez} [Sel. Math., New Ser. 20, No. 2, 491--584 (2014; Zbl 1294.17012)].
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