Orbits by the up-down action of braid diagrams
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929643357995008 |
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| author | Negi, Komal Shimizu, Ayaka Yaguchi, Yoshiro Prabhakar, Madeti |
| author_facet | Negi, Komal Shimizu, Ayaka Yaguchi, Yoshiro Prabhakar, Madeti |
| contents | The set of all virtual or classical braid diagrams forms a monoid and gives a natural monoid action on a direct product of ${\mathbb Z}$ called the up-down action. In this paper, we determine the orbit of every tuple of ${\mathbb Z}$ under the up-down action of virtual or classical braid diagrams. Moreover, we determine the orbit for irreducible braid diagrams. We also consider the isotropy submonoid and give a condition for a braid diagram to admit an up-down coloring to its closure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_12553 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Orbits by the up-down action of braid diagrams Negi, Komal Shimizu, Ayaka Yaguchi, Yoshiro Prabhakar, Madeti Geometric Topology 57K10, 57K12 The set of all virtual or classical braid diagrams forms a monoid and gives a natural monoid action on a direct product of ${\mathbb Z}$ called the up-down action. In this paper, we determine the orbit of every tuple of ${\mathbb Z}$ under the up-down action of virtual or classical braid diagrams. Moreover, we determine the orbit for irreducible braid diagrams. We also consider the isotropy submonoid and give a condition for a braid diagram to admit an up-down coloring to its closure. |
| title | Orbits by the up-down action of braid diagrams |
| topic | Geometric Topology 57K10, 57K12 |
| url | https://arxiv.org/abs/2412.12553 |