论文标题
RII的打结预测数
RII number of knot projections
论文作者
论文摘要
每个结的投影都可以通过使用类型1、2和3的变形来简化琐碎的球形曲线，这是打结图中类型1、2和3的类比。我们介绍了一个打结投影的RII数量，即这种序列中负2的最小变形数。根据定义，它在类型1和3的变形下是不变的。这是由Östlund猜想的：1和3型的变形足以描述从圆圈中任何一般圆的综合沉浸在二维平面上的同型，以嵌入圆圈（2001）（2001），这意味着RII始终是RIII始终是均值的。但是，hagge和Yazinski通过以16个双点显示了第一个反例来反驳了猜想，这意味着RII数字是不平凡的。本文表明，RII号可以是任何非负数。
Every knot projection is simplified to the trivial spherical curve not increasing double points by using deformations of types 1, 2, and 3 which are analogies of Reidemeister moves of types 1, 2, and 3 on knot diagrams. We introduce RII number of a knot projection that is the minimum number of deformations of negative type 2 among such sequences. By definition, it is invariant under deformations of types 1 and 3. This is motivated by Östlund conjecture: Deformations of type 1 and 3 are sufficient to describe a homotopy from any generic immersion of a circle in a two dimensional plane to an embedding of the circle (2001), which implies RII number always would be zero. However, Hagge and Yazinski disproved the conjecture by showing the first counterexample with 16 double points, which implies that RII number is nontrivial. This paper shows that RII number can be any nonnegative number.
