Invariants of knot diagrams and relations among Reidemeister moves
Invariants of knot diagrams and relations among Reidemeister moves
复制标题
结图的不变量和 Reidemeister 动作之间的关系
DOI：
10.1142/s0218216501001402
复制
发表时间：
2000
影响因子：
0.5
通讯作者：
Olof
中科院分区：
文献类型：
--
作者：
Olof
本文介绍了一种最精细的雷德迈斯特动作分类法。特别是，这种分类区分了一些Ω3-移动，它们的区别仅在于移动中涉及的三条链在结上的排序方式。为了将同位素纽结的纽结图相互转换，一般必须使用至少两个不同类的Ω3-移动。为了证明这一点，引入了仅在Ω3-移动下跳跃的结图不变量。同位素纽结的纽结图可以通过一系列里德迈斯特移动连接，在总共24个类别中只有6个类别。这一结果可应用于纽结理论，简化数学纽结不变量不变性的证明。特别地，给出了高斯图上的函数定义纽结不变量的一个判据。
In this paper a classification of Reidemeister moves, which is the most refined, is introduced. In particular, this classification distinguishes some Ω3-moves that only differ in how the three strands that are involved in the move are ordered on the knot. To transform knot diagrams of isotopic knots into each other one must in general use Ω3-moves of at least two different classes. To show this, knot diagram invariants that jump only under Ω3-moves are introduced. Knot diagrams of isotopic knots can be connected by a sequence of Reidemeister moves of only six, out of the total of 24, classes. This result can be applied in knot theory to simplify proofs of invariance of diagrammatical knot invariants. In particular, a criterion for a function on Gauss diagrams to define a knot invariant is presented.