The splittability and triviality of 3-bridge links
The splittability and triviality of 3-bridge links
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三桥链路的可拆分性和简单性
DOI：
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发表时间：
1985
期刊：
影响因子：
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通讯作者：
K. Okita
中科院分区：
文献类型：
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作者：
Seiya Negami;K. Okita
本文讨论了在一般情况下简化链节三桥投影的一种方法，即波浪移动法，并说明了从三桥链节的波浪移动投影中可以识别出它们的性质。特别地，它将被证明，每一个3-桥投影的可裂链接或平凡结可以转化为一个不连通的一个或一个六边形，分别由一个有限序列的波移动。通过S3的2重分支覆盖的概念，可以得出S2 × S2 # L（p，q）或S3的每个亏格2 Heegaard图都可以通过一个有限的操作序列（也称为波移动）变换成一个特定的标准型。
A method to simplify 3-bridge projections of links and knots, called a wate move, is discussed in general situation and it is shown what kind of properties of 3-bridge links and knots can be recognized from their projections by wave moves. In particular, it will be proved that every 3-bridge projection of a splittable link or a trivial knot can be transformed into a disconnected one or a hexagon, respectively, by a finite sequence of wave moves. As its translation via the concept of 2-fold branched coverings of S3, it follows that every genus 2 Heegaard diagram of S2 X S2 # L(p, q) or S3 can be transformed into one of specific standard forms by a finite sequence of operations also called wave moves.