论文标题
在（1，3）下的非平凡结投影上
On a nontrivial knot projection under (1, 3) homotopy
论文作者
论文摘要
在2001年，Östlund提出了一个问题：1和3型的雷迪德移动是否足以描述从圆圈中任何一般嵌入二维平面到圆圈嵌入的同质性的移动？这个问题的积极答案被视为猜想（Östlund猜想）。在2014年，hagge和Yazinski通过显示第一个反例以最小的交叉数量16来反映了猜想。此示例自然地扩展到反例，甚至给定的最小交叉数量超过14个。本文获得了第一个对示例的最小交叉数字，而示例最少15个示例。自然而然地将其与给定的数字相比，以奇怪的是奇怪的数字。
In 2001, Östlund 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 (Östlund 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.
