Some links with non-adequate minimal-crossing diagrams
Some links with non-adequate minimal-crossing diagrams
复制标题
一些带有不充分的最小交叉图的链接
DOI：
10.1017/s030500410007537x
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发表时间：
1992
影响因子：
0.8
通讯作者：
Makoto Yamamoto
中科院分区：
文献类型：
--
作者：
Masao Hara;Makoto Yamamoto
为了研究从图表中导出的链接不变量，最近新的链接多项式不变量发挥了重要作用。 Murasugi6、7、Kauffman3 和 Thistlethwaite 9 独立地表明，链路的正确连通交替图中的交叉数是链路的最小交叉数，并且图的扭转是不变的。 Murasugi 8 还确定了环面链接的最小交叉数。在5中，Lickorish和Thistlethwaite引入了充分链路图的概念，并表明半交替链路充分图中的交叉数是链路的最小交叉数。他们还确定了几乎所有 Montesinos 链路的最小交叉数量。在本文中，我们表明，对于一些由板和辫子表示的不充分的链接，图中的交叉数是链接的最小交叉数。
To investigate invariants of links derived from their diagrams, the recent new polynomial invariants of links play important roles. Murasugi6, 7, Kauffman3 and Thistlethwaite 9 independently showed that the number of crossings in a proper connected alternating diagram of a link is the minimal-crossing number of the link and that the writhe of the diagram is invariant. Murasugi 8 also determined the minimal-crossing number of torus links. In 5, Lickorish and Thistlethwaite introduced the concept of an adequate link diagram and showed that the number of crossings in an adequate diagram of a semi-alternating link is the minimal-crossing number of the link. They also determined the minimal-crossing number of almost all Montesinos links. In this paper we show that for some links represented by plats and braids which are not adequate, the numbers of crossings in the diagrams are the minimal-crossing numbers of the links.