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Intégrale de Kontsevich elliptique et enchevêtrements en genre supérieur

Abstract : We construct a functorial invariant of tangles embedded in the thickened torus. This invariant generalizes the Kontsevich integral, and can be analytically derivated from a universal version of the elliptic Knizhnik-Zamolodchikov-Bernard equation. The main part of the thesis is devoted to the combinatorial version of its construction, using the notion of « elliptic associator » introduced by Enriquez. A key ingredient is a universal property satisfied by the category of framed tangles in the torus. This universal property is established in the language of monoidal categories, and extends Reshetikhin-Turaev-Shum's coherence theorem to the case of framed tangles in any closed genus g surface.
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Philippe Humbert. Intégrale de Kontsevich elliptique et enchevêtrements en genre supérieur. Mathématiques générales [math.GM]. Université de Strasbourg, 2012. Français. ⟨NNT : 2012STRAD042⟩. ⟨tel-00762209v2⟩

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