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math.QA2022
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…
math.QA2021
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…
math.QA2020
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"…