40 citations · 67 across the 18 of their papers we have counts for
23 papers
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…
Genus Zero Kashiwara-Vergne Solutions from Braids
Zsuzsanna Dancso, Iva Halacheva, Guillaume Laplante-Anfossi +2
Using the language of moperads -- monoids in the category of right modules over an operad -- we reinterpret the Alekseev--Enriquez--Torossian construction of Kashiwara--Vergne (KV)…
A Reidemeister Theorem for Solid Ribbon Torus Links
Zsuzsanna Dancso, Thomas Malliaras Gavrielatos
A complete Reidemeister characterisation of welded links is a long-standing open problem. We present a Reidemeister Theorem for a related class of four-dimensional links, solid rib…
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…
Mutation, surface graphs, and alternating links in surfaces
Hans U. Boden, Zsuzsanna Dancso, Damian J. Lin +1
In this paper, we study alternating links in thickened surfaces in terms of the lattices of integer flows on their Tait graphs. We use this approach to give a short proof of the fi…
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…
Lattice of Integer Flows and the Poset of Strongly Connected Orientations for Regular Matroids
Zsuzsanna Dancso, Jongmin Lim
A 2010 result of Amini provides a way to extract information about the structure of the graph from the geometry of the Voronoi polytope of the lattice of integer flows (which deter…
Arc diagrams on 3-manifold spines
Jack Brand, Benjamin A. Burton, Zsuzsanna Dancso +3
We develop a theory of link projections to trivalent spines of 3-manifolds. We prove a Reidemeister Theorem providing a set of combinatorial moves sufficient to relate the projecti…
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"…
Over then Under Tangles
Dror Bar-Natan, Zsuzsanna Dancso, Roland van der Veen
Over-then-Under (OU) tangles are oriented tangles whose strands travel through all of their over crossings before any under crossings. In this paper we discuss the idea of gliding:…
Deletion-contraction triangles for Hausel-Proudfoot varieties
Zsuzsanna Dancso, Michael McBreen, Vivek Shende
To a graph, Hausel and Proudfoot associate two complex manifolds, B and D, which behave, respectively like moduli of local systems on a Riemann surface, and moduli of Higgs bundles…
Koszul Algebras and Flow Lattices
Zsuzsanna Dancso, Anthony M. Licata
We provide a homological algebraic realization of the lattices of integer cuts and integer flows of graphs. To a finite 2-edge-connected graph with a spanning tree , we asso…
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…
What is a Singular Knot?
Zsuzsanna Dancso
A singular knot is an immersed circle in with finitely many transverse double points. The study of singular knots was initially motivated by the study of Vassiliev…
A construction of the graphic matroid from the lattice of integer flows
Zsuzsanna Dancso, Stavros Garoufalidis
The lattice of integer flows of a graph is known to determine the graph up to 2-isomorphism (work of Su--Wagner and Caporaso--Viviani). In this paper we give an algorithmic constru…
Finite Type Invariants of w-Knotted Objects I: w-Knots and the Alexander Polynomial
Dror Bar-Natan, Zsuzsanna Dancso
This is the first in a series of papers studying w-knotted objects (w-knots, w-braids, w-tangles, etc.), which make a class of knotted objects which is {w}ider but {w}eaker than th…
Finite Type Invariants of w-Knotted Objects II: Tangles, Foams and the Kashiwara-Vergne Problem
Dror Bar-Natan, Zsuzsanna Dancso
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…
Finite Type Invariants of w-Knotted Objects: From Alexander to Kashiwara and Vergne
Dror Bar-Natan, Zsuzsanna Dancso
This preprint was split in two and became the first two parts of a four-part series (arXiv:1405.1956, arXiv:1405:1955, and two in preparation). The remaining relevance of this prep…
Odd Khovanov Homology for Hyperplane Arrangements
Zsuzsanna Dancso, Anthony Licata
We define several homology theories for central hyperplane arrangements, categorifying well-known polynomial invariants including the characteristic polynomial, Poincare polynomial…
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…
On the Kontsevich integral for knotted trivalent graphs
Zsuzsanna Dancso
We construct an extension of the Kontsevich integral of knots to knotted trivalent graphs, which commutes with orientation switches, edge deletions, edge unzips, and connected sums…