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arXiv · 2108.04557

Brauer diagrams, modular operads, and a graphical nerve theorem for circuit algebras

Sophie Raynor
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Abstract

Circuit algebras, used in the study of finite-type knot invariants, are a symmetric analogue of Jones's planar algebras. They are very closely related to circuit operads, which are a variation of modular operads admitting an extra monoidal product. This paper gives a description of circuit algebras in terms categories of Brauer diagrams. An abstract nerve theorem for circuit operads -- and hence circuit algebras -- is proved using an iterated distributive law, and an existing nerve theorem for modular operads.

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Sophie Raynor. 2021-08-10. Brauer diagrams, modular operads, and a graphical nerve theorem for circuit algebras. https://arxiv.org/abs/2108.04557

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