The bridge number of surface links and kei colorings
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866916193556758528 |
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| author | Sato, Kouki Tanaka, Kokoro |
| author_facet | Sato, Kouki Tanaka, Kokoro |
| contents | Meier and Zupan introduced bridge trisections of surface links in $S^4$ as a 4-dimensional analogue to bridge decompositions of classical links, which gives a numerical invariant of surface links called the bridge number. We prove that there exist infinitely many surface knots with bridge number $n$ for any integer $n \geq 4$. To prove it, we use colorings of surface links by keis and give lower bounds for the bridge number of surface links. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2004_07056 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The bridge number of surface links and kei colorings Sato, Kouki Tanaka, Kokoro Geometric Topology 57K45 (Primary) 57K12 (Secondary) Meier and Zupan introduced bridge trisections of surface links in $S^4$ as a 4-dimensional analogue to bridge decompositions of classical links, which gives a numerical invariant of surface links called the bridge number. We prove that there exist infinitely many surface knots with bridge number $n$ for any integer $n \geq 4$. To prove it, we use colorings of surface links by keis and give lower bounds for the bridge number of surface links. |
| title | The bridge number of surface links and kei colorings |
| topic | Geometric Topology 57K45 (Primary) 57K12 (Secondary) |
| url | https://arxiv.org/abs/2004.07056 |