In this paper, we describe a surprising link between the theory of the Goldman–Turaev Lie
bialgebra on surfaces of genus zero and the Kashiwara–Vergne (KV) problem in Lie theory …

A correspondence between three-dimensional flat connections and constant curvature four-
dimensional simplices is used to give a novel quantization of geometry via complex SL (2 …

This is the second in a series of papers dedicated to studying w-knots, and more generally,
w-knotted objects (w-braids, w-tangles, etc.). These are classes of knotted objects that are w …

Building on recently established enumerative connections between lambda calculus and the
theory of embedded graphs (or" maps"), this paper develops an analogy between typing (of …

arXiv:1309.7155v2 [math.GT] 11 May 2014 Page 1 arXiv:1309.7155v2 [math.GT] 11 May
2014 FINITE TYPE INVARIANTS OF W-KNOTTED OBJECTS: FROM ALEXANDER TO …

This is the second in a series of papers dedicated to studying w-knots, and more generally,
w-knotted objects (w-braids, w-tangles, etc.). These are classes of knotted objects that are …

An involutive Lie bialgebra induces a Batalin-Vilkovisky operator on its exterior algebra. We
introduce a graded generalization of the necklace Lie bialgebra, which depends on a choice …

This is the third in a series of papers studying the finite type invariants of various w-knotted
objects and their relationship to the Kashiwara-Vergne problem and Drinfel'd associators. In …

Dans cette thèse, on définit un invariant fonctoriel d'enchevêtrements dans le tore épaissi
qui généralise l'intégrale de Kontsevich. Cet invariant est tout d'abord construit …

We define a category v 𝒯 of tangles diagrams drawn on surfaces with boundaries. On the
one hand, we show that there is a natural functor from the category of virtual tangles to v 𝒯 …