Dynamics of quandle orders
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917847066738688 |
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| author | Jibiki, Chihaya |
| author_facet | Jibiki, Chihaya |
| contents | We construct a continuous map from the space of orders on quandles to the space of quandle actions on one-manifolds, providing an answer to a question posed by Idrissa Ba and Mohamed Elhamdadi. As an application of this map, we characterize isolated orders on quandles in terms of strong rigidity. As another application, we prove that there is no isolated right order on the free quandles, except for specific cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_21476 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamics of quandle orders Jibiki, Chihaya Geometric Topology Dynamical Systems 06F15 (Primary) 37E10, 57K12 (Secondary) We construct a continuous map from the space of orders on quandles to the space of quandle actions on one-manifolds, providing an answer to a question posed by Idrissa Ba and Mohamed Elhamdadi. As an application of this map, we characterize isolated orders on quandles in terms of strong rigidity. As another application, we prove that there is no isolated right order on the free quandles, except for specific cases. |
| title | Dynamics of quandle orders |
| topic | Geometric Topology Dynamical Systems 06F15 (Primary) 37E10, 57K12 (Secondary) |
| url | https://arxiv.org/abs/2410.21476 |