Minimal generating sets of rotational Reidemeister moves
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908412857548800 |
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| author | Becerra, Jorge van Helden, Kevin |
| author_facet | Becerra, Jorge van Helden, Kevin |
| contents | Rotational tangle diagrams have been proven to be extremely important in the study of quantum invariants, as they provide a natural passage between topology and quantum algebra. In this paper, we give a detailed description of several generating sets of rotational Reidemeister moves for rotational diagrams of both unframed and framed tangles. In particular, we prove that the minimal number of moves needed to generate all oriented unframed (resp. framed) rotational Reidemeister moves is 8 (resp. 9). The latter implies that a minimal generating set of Reidemeister moves for oriented, framed links contains 5 moves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15628 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Minimal generating sets of rotational Reidemeister moves Becerra, Jorge van Helden, Kevin Geometric Topology 57K10, 57K16 Rotational tangle diagrams have been proven to be extremely important in the study of quantum invariants, as they provide a natural passage between topology and quantum algebra. In this paper, we give a detailed description of several generating sets of rotational Reidemeister moves for rotational diagrams of both unframed and framed tangles. In particular, we prove that the minimal number of moves needed to generate all oriented unframed (resp. framed) rotational Reidemeister moves is 8 (resp. 9). The latter implies that a minimal generating set of Reidemeister moves for oriented, framed links contains 5 moves. |
| title | Minimal generating sets of rotational Reidemeister moves |
| topic | Geometric Topology 57K10, 57K16 |
| url | https://arxiv.org/abs/2506.15628 |