The number of Reidemeister moves needed for unknotting
The number of Reidemeister moves needed for unknotting
复制标题
解开结所需的雷德迈斯特动作次数
DOI：
10.1090/s0894-0347-01-00358-7
复制
发表时间：
1998
影响因子：
3.9
通讯作者：
J. Lagarias
中科院分区：
文献类型：
--
作者：
J. Hass;J. Lagarias
有一个正的常数c1，使得对于任何表示解结的图D，有一个最多2个c1 n的Reidemeister移动序列将其转换为平凡结图，其中n是D中的交叉数。一个类似的结果也适用于嵌入在紧致的、可定向的、三角化的PL 3-流形M的内部的1-骨架中的多边形纽结K上的初等移动。有一个正的常数c2，使得对于每个t1，如果M由t个四面体组成，并且K是无结的，那么M中有一个至多2个c2 t基本移动的序列，它将K变换为包含在M的一个四面体内的三角形。我们得到了c1和c2的显式值。
There is a positive constant c1 such that for any diagram D representing the unknot, there is a sequence of at most 2 c1n Reidemeister moves that will convert it to a trivial knot diagram, where n is the number of crossings in D. A similar result holds for elementary moves on a polygonal knot K embedded in the 1-skeleton of the interior of a compact, orientable, triangulated P L 3-manifold M. There is a positive constant c2 such that for each t � 1, if M consists of t tetrahedra, and K is unknotted, then there is a sequence of at most 2 c 2t elementary moves in M which transforms K to a triangle contained inside one tetrahedron of M. We obtain explicit values for c1 and c2.