A new algorithm for recognizing the unknot
A new algorithm for recognizing the unknot
复制标题
一种识别无结的新算法
DOI：
10.2140/gt.1998.2.175
复制
发表时间：
1998
影响因子：
2
通讯作者：
M. D. Hirsch
中科院分区：
文献类型：
--
作者：
J. Birman;M. D. Hirsch
The topological underpinnings are presented for a new algorithm which answers the question: `Is a given knot the unknot?' The algorithm uses the braid foliation technology of Bennequin and of Birman and Menasco. The approach is to consider the knot as a closed braid, and to use the fact that a knot is unknotted if and only if it is the boundary of a disc with a combinatorial foliation. The main problems which are solved in this paper are: how to systematically enumerate combinatorial braid foliations of a disc; how to verify whether a combinatorial foliation can be realized by an embedded disc; how to find a word in the the braid group whose conjugacy class represents the boundary of the embedded disc; how to check whether the given knot is isotopic to one of the enumerated examples; and finally, how to know when we can stop checking and be sure that our example is not the unknot.
