40 citations · 67 across the 18 of their papers we have counts for
8 papers · 1 filter
Goldman-Turaev formality from the Kontsevich integral
Dror Bar-Natan, Zsuzsanna Dancso, Tamara Hogan +2
We present a new solution to the formality problem for the framed Goldman--Turaev Lie bialgebra, constructing Goldman-Turaev homomorphic expansions (formality isomorphisms) from th…
Kashiwara-Vergne solutions degree by degree
Zsuzsanna Dancso, Iva Halacheva, Guillaume Laplante-Anfossi +1
We show that solutions to the Kashiwara-Vergne problem can be extended degree by degree. This can be used to simplify the computation of a class of Drinfel'd associators, which und…
A knot-theoretic approach to comparing the Grothendieck-Teichmüller and Kashiwara-Vergne groups
Zsuzsanna Dancso, Tamara Hogan, Marcy Robertson
Homomorphic expansions are combinatorial invariants of knotted objects, which are universal in the sense that all finite-type (Vassiliev) invariants factor through them. Homomorphi…
A topological characterisation of the Kashiwara-Vergne groups
Zsuzsanna Dancso, Iva Halacheva, Marcy Robertson
In 2017 Bar-Natan and the first author showed that solutions to the Kashiwara--Vergne equations are in bijection with certain knot invariants: homomorphic expansions of welded foam…
Circuit algebras are wheeled props
Zsuzsanna Dancso, Iva Halacheva, Marcy Robertson
Circuit algebras, introduced by Bar-Natan and the first author, are a generalization of Jones's planar algebras, in which one drops the planarity condition on "connection diagrams"…
Ribbon 2-Knots, , and Duflo's Theorem for Arbitrary Lie Algebras
Dror Bar-Natan, Zsuzsanna Dancso, Nancy Scherich
We explain a direct topological proof for the multiplicativity of Duflo isomorphism for arbitrary finite dimensional Lie algebras, and derive the explicit formula for the Duflo map…
Homomorphic expansions for knotted trivalent graphs
Dror Bar-Natan, Zsuzsanna Dancso
It had been known since old times [MO, Da] that there exists a universal finite type invariant ("an expansion") Z^{old} for Knotted Trivalent Graphs (KTGs), and that it can be chos…
Pentagon and hexagon equations following Furusho
Dror Bar-Natan, Zsuzsanna Dancso
In [F] H. Furusho proves the beautiful result that of the three defining equations for associators, the pentagon implies the two hexagons (see also [W]). In this note we present a…