Minimal crossing number implies minimal supporting genus
| Autor: | Boden, Hans U., Rushworth, William |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Bull. Lond. Math. Soc. 53 (2021), no. 4, 1174-1184 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1112/blms.12491 |
| Popis: | A virtual link may be defined as an equivalence class of diagrams, or alternatively as a stable equivalence class of links in thickened surfaces. We prove that a minimal crossing virtual link diagram has minimal genus across representatives of the stable equivalence class. This is achieved by constructing a new parity theory for virtual links. As corollaries, we prove that the crossing, bridge, and ascending numbers of a classical link do not decrease when it is regarded as a virtual link. This extends corresponding results in the case of virtual knots due to Manturov and Chernov. Comment: 10 pages, 3 figures. Comments welcome. Proof of Theorem 10 reorganised |
| Databáze: | arXiv |
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