论文标题
（1，2）和弱（1，3）结的同型
(1, 2) and weak (1, 3) homotopies on knot projections
论文作者
论文摘要
在本文中，我们获得了必要和充分的条件，即两个结的投影与第一和第二平面雷迪德式移动的有限序列相关（定理1）。我们还考虑了一种称为弱（1，3）同喻的等效关系。这种等效关系是通过第一个平坦的雷德式移动和第三个扁平雷迪德斯的移动之一发生的。我们介绍了一张地图，将弱（1，3）同质类别发送给共结（第3节）。使用地图，我们确定在弱（1，3）同型（推论3）下进行了哪些结突显。
In this paper, we obtain the necessary and sufficient condition that two knot projections are related by a finite sequence of the first and second flat Reidemeister moves (Theorem 1). We also consider an equivalence relation that is called weak (1, 3) homotopy. This equivalence relation occurs by the first flat Reidemeister move and one of the third flat Reidemeister moves. We introduce a map sending weak (1, 3) homotopy classes to knot isotopy classes (Sec. 3). Using the map, we determine which knot projections are trivialized under weak (1, 3) homotopy (Corollary 3).
