Circuit algebras are wheeled props

@article{Dancso2020CircuitAA,
  title={Circuit algebras are wheeled props},
  author={Zsuzsanna Dancso and I. Halacheva and M. Robertson},
  journal={arXiv: Quantum Algebra},
  year={2020}
}
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". They provide a useful language for the study of virtual and welded tangles in low-dimensional topology. In this note, we present the circuit algebra analogue of the well-known classification of planar algebras as pivotal categories with a self-dual generator. Our main theorem is that there is an equivalence of… Expand
Brauer diagrams, modular operads, and a graphical nerve theorem for circuit algebras
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In [BND17] Bar-Natan and the first author show that solutions to the Kashiwara–Vergne equations are in bijection with certain knot invariants: homomorphic expansions of welded foams. Welded foams areExpand

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