Conjugation and the prime decomposition of knots in closed, oriented 3-manifolds
Conjugation and the prime decomposition of knots in closed, oriented 3-manifolds
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封闭定向 3 流形中结的共轭和素数分解
DOI：
10.1090/s0002-9947-1989-0997679-2
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发表时间：
1989
影响因子：
1.3
通讯作者：
Katura Miyazaki
中科院分区：
文献类型：
--
作者：
Katura Miyazaki
.本文考虑了闭定向三维流形中纽结的素分解。(For通过使用标准的最内层圆盘图，可以容易地证明素数分解的唯一性。我们定义了一个新的关系，共轭，在封闭的定向3-流形定向纽结之间，并证明了以下结果。（1）粗略地说，素分解在共轭之前是唯一确定的，（2）存在素结á？在SlxS 2中，比如说？= 3#X2，如果^^是^2）的共轭，以及（3）如果纽结3#X2，有一个不含31的素分解，则它是X的唯一素分解。
. In this paper we consider the prime decomposition of knots in closed, oriented 3-manifolds. (For classical knots one can easily prove the uniqueness of prime decomposition by using a standard innermost disk argu-ment.) We define a new relation, conjugation, between oriented knots in closed, oriented 3-manifolds and prove the following results. ( 1 ) The prime decomposition is, roughly speaking, uniquely determined up to conjugation, (2) there is a prime knot á? in SlxS2 suchthat âl#3?\ = 3¡#X2 if ^¡ is a conjugation of ^2 ) and (3) if a knot 3? has a prime decomposition which does not contain 31, then it is the unique prime decomposition of X .