5 papers
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"…
Modular operads and the nerve theorem
Philip Hackney, Marcy Robertson, Donald Yau
We describe a category of undirected graphs which comes equipped with a faithful functor into the category of (colored) modular operads. The associated singular functor from modula…
A graphical category for higher modular operads
Philip Hackney, Marcy Robertson, Donald Yau
We present a homotopy theory for a weak version of modular operads whose compositions and contractions are only defined up to homotopy. This homotopy theory takes the form of a Qui…