On a nontrivial knot projection under (1, 3) homotopy
| Autor: | Ito, Noboru, Takimura, Yusuke |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Topology Appl. 210 (2016), 22--28 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.topol.2016.07.008 |
| Popis: | In 2001, \"Ostlund formulated the question: are Reidemeister moves of types 1 and 3 sufficient to describe a homotopy from any generic immersion of a circle in a two-dimensional plane to an embedding of the circle? The positive answer to this question was treated as a conjecture (\"Ostlund conjecture). In 2014, Hagge and Yazinski disproved the conjecture by showing the first counterexample with a minimal crossing number of 16. This example is naturally extended to counterexamples with given even minimal crossing numbers more than 14. This paper obtains the first counterexample with a minimal crossing number of 15. This example is naturally extended to counterexamples with given odd minimal crossing numbers more than 13. Comment: 8 pages, 14 figures |
| Databáze: | arXiv |
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