论文标题
结的强度和弱（1，2）在结预测和新不变性上
Strong and weak (1, 2) homotopies on knot projections and new invariants
论文作者
论文摘要
当打结投影的方向任意提供时，可以将打结投影的每一个平面移动分解为两种类型，分别彻底或直接的自分类修改，称为强或弱。此外，我们介绍了强度和弱（1，2）同义的概念；我们定义了两个结的强烈（弱）（弱）（1，2）同时性时，并且仅当两个结次突起通过有限的第一和强（sever）第二flat flat reidemister移动的有限序列相关。本文提供了一种新的必要条件，即两个结的预测并不强（1，2）同型。同样，我们在弱（1，2）同拷贝情况下获得了一种新的必要条件。我们还定义了一个新的整数增值强（1，2）同型不变性。使用它，我们表明，在强（1，2）同拷贝下可以轻描淡写的一组非平凡的原始打结投影集与弱（1，2）同型均不相交。我们还研究了新不变的拓扑特性，并进行了概括，对我们的不变性和不变性的比较以及不变的表。
Every second flat Reidemeister move of knot projections can be decomposed into two types thorough an inverse or direct self-tangency modification, respectively called strong or weak, when orientations of the knot projections are arbitrarily provided. Further, we introduce the notions of strong and weak (1, 2) homotopies; we define that two knot projections are strongly (resp. weakly) (1, 2) homotopic if and only if two knot projections are related by a finite sequence of first and strong (resp. weak) second flat Reidemeister moves. This paper gives a new necessary and sufficient condition that two knot projections are not strongly (1, 2) homotopic. Similarly, we obtain a new necessary and sufficient condition in the weak (1, 2) homotopy case. We also define a new integer-valued strong (1, 2) homotopy invariant. Using it, we show that the set of the non-trivial prime knot projections without 1-gons that can be trivialized under strong (1, 2) homotopy is disjoint from that of weak (1, 2) homotopy. We also investigate topological properties of the new invariant and give its generalization, a comparison of our invariants and Arnold invariants, and a table of invariants.
