The skein polynomial of closed 3-braids
The skein polynomial of closed 3-braids
复制标题
闭合3辫子的绞纱多项式
DOI：
10.1515/crll.2003.088
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
A. Stoimenow
中科院分区：
文献类型：
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作者：
A. Stoimenow
利用3股辫群的带表示，证明了3股辫链的亏格可以从它们的绞链多项式中读出。给出了一些应用，特别是Morton不等式的一个简单证明和判定某些多项式（如9_{49}的多项式）不被3-辫环所接纳的一个条件.最后，对辫状指数为3的交错链环进行了分类.
Using the band representation of the 3-strand braid group, it is shown that the genus of 3-braid links can be read off their skein polynomial. Some applications are given, in particular a simple proof of Morton's conjectured inequality and a condition to decide that some polynomials, like the one of 9_{49}, are not admitted by 3-braid links. Finally, alternating links of braid index 3 are classified.