Classification of algebraic tangles
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912318234820608 |
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| author | Gren, Bartosz Ambrozy Sulkowska, Joanna Ida Gabrovšek, Boštjan |
| author_facet | Gren, Bartosz Ambrozy Sulkowska, Joanna Ida Gabrovšek, Boštjan |
| contents | We study algebraic tangles as fundamental components in knot theory, developing a systematic approach to classify and tabulate prime tangles using a novel canonical representation. The canonical representation enables us to distinguish mutant tangles, which fills the gaps in previous classifications. Moreover, we increase the classification of prime tangles up to 14 crossings and analyze tangle symmetry groups. We provide a database of our results: https://tangleinfo.cent.uw.edu.pl. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_06901 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Classification of algebraic tangles Gren, Bartosz Ambrozy Sulkowska, Joanna Ida Gabrovšek, Boštjan Geometric Topology Algebraic Topology Group Theory Number Theory 57K10 (Primary) 57K12, 11D68, 20C30 (Secondary) We study algebraic tangles as fundamental components in knot theory, developing a systematic approach to classify and tabulate prime tangles using a novel canonical representation. The canonical representation enables us to distinguish mutant tangles, which fills the gaps in previous classifications. Moreover, we increase the classification of prime tangles up to 14 crossings and analyze tangle symmetry groups. We provide a database of our results: https://tangleinfo.cent.uw.edu.pl. |
| title | Classification of algebraic tangles |
| topic | Geometric Topology Algebraic Topology Group Theory Number Theory 57K10 (Primary) 57K12, 11D68, 20C30 (Secondary) |
| url | https://arxiv.org/abs/2504.06901 |