Biracks and Switch Braid Quivers

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...

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Bibliographic Details
Published in:arXiv.org 2024-06
Main Authors: Chao-Haft, Max, Nelson, Sam
Format: Article
Language:English
Subjects:
Automorphisms
Braid theory
Braiding
Invariants
Permutations
Polynomials
Representations
Switches
Online Access:Get full text
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Summary: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.
ISSN:2331-8422