Biracks and Switch Braid Quivers
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866911936874020864 |
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| author | Chao-Haft, Max Nelson, Sam |
| author_facet | Chao-Haft, Max Nelson, Sam |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_10787 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Biracks and Switch Braid Quivers Chao-Haft, Max Nelson, Sam Geometric Topology Quantum Algebra 57K12 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. |
| title | Biracks and Switch Braid Quivers |
| topic | Geometric Topology Quantum Algebra 57K12 |
| url | https://arxiv.org/abs/2110.10787 |