论文标题
结的强和弱（1，3）的同型
Strong and weak (1, 3) homotopies on knot Projections
论文作者
论文摘要
强和弱（1，3）同型是结的等效关系，这是由第一个扁平式移动和第三种扁平式雷迪德式移动的两种不同类型的两种类型的类型所定义的。在本文中，我们介绍了跨和弦编号，即和弦图的双点的最小数量。交叉和弦数量会引起强（1，3）不变。我们表明，哈纳基的琐碎数字是一个弱（1，3）不变的。我们将使用交叉和弦数字和双点的正分辨率进行完整的打结投影分类，直到第一个平坦的Reidemester Moves。当且仅当仅当仅通过第一个平坦的Reidemeister移动时，两个结的打结投影都弱（1，3）同等（1，3）同型等效物。最后，我们确定了包含琐碎的结投影和其他类结突击的强（1，3）同副率等效类。
Strong and weak (1, 3) homotopies are equivalence relations on knot projections, defined by the first flat Reidemeister move and each of two different types of the third flat Reidemeister moves. In this paper, we introduce the cross chord number that is the minimal number of double points of chords of a chord diagram. Cross chord numbers induce a strong (1, 3) invariant. We show that Hanaki's trivializing number is a weak (1, 3) invariant. We give a complete classification of knot projections having trivializing number two up to the first flat Reidemeister moves using cross chord numbers and the positive resolutions of double points. Two knot projections with trivializing number two are both weak (1, 3) homotopy equivalent and strong (1, 3) homotopy equivalent if and only if they can be related by only the first flat Reidemeister moves. Finally, we determine the strong (1, 3) homotopy equivalence class containing the trivial knot projection and other classes of knot projections.
