Biracks and Switch Braid Quivers

Max Chao-Haft; Sam Nelson

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arXiv · 2110.10787

Biracks and Switch Braid Quivers

Max Chao-Haft·Sam Nelson

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Abstract

We consider birack and switch colorings of braids. We define a switch structure on the set of permutation representations of the braid group and consider when such a representation is a switch automorphism. We define quiver-valued invariants of braids using finite switches and biracks and use these to categorify the birack 2-cocycle invariant for braids. We obtain new polynomial invariants of braids via decategorification of these quivers.

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Max Chao-Haft, Sam Nelson. 2021-10-20. Biracks and Switch Braid Quivers. https://arxiv.org/abs/2110.10787

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