An irreducible 4-string braid with unknotted closure
An irreducible 4-string braid with unknotted closure
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不可缩减的 4 串编织物，带无结闭合
DOI：
10.1017/s0305004100060540
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发表时间：
1983
影响因子：
0.8
通讯作者：
H. Morton
中科院分区：
文献类型：
--
作者：
H. Morton
S3中的每个定向纽结或链环都可以用多种方式表示为n个弦上的辫子群β∈Bn的闭包，其中辫子β∈Bn，γ∈Bm称为闭包等价的当且等价于定向纽结.这是马尔可夫的一个众所周知的结果，例如参见(L)，β和γ是闭包等价的当且仅当存在基本(马尔可夫)运动序列，其中β∈Bn被(A)Bn中的共轭或(C)β1∈Bn−1替换，其中，重复该过程直到达到γ。
Every oriented knot or link in S3 can be represented in many ways as the closure of a braid β ∈ Bn, the braid group on n strings, for some n. Braids β ∈ Bn, γ ∈ Bm are called closure-equivalent if and are equivalent as oriented knots. It is a well-known result of Markov, see, for example, (l), that β and γ are closure equivalent if and only if there is a sequence of elementary (Markov) moves in which β ∈ Bn is replaced by (a) a conjugate in Bn, or , or (c) β1 ∈ Bn−1, where , and the process repeated until γ is reached.