STUDYING LINKS VIA CLOSED BRAIDS I
STUDYING LINKS VIA CLOSED BRAIDS I
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通过闭合辫子研究链接 I
DOI：
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发表时间：
1992
期刊：
影响因子：
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通讯作者：
W. Menasco
中科院分区：
文献类型：
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作者：
J. Birman;W. Menasco
本文是研究定向三维空间中定向链环类型l的闭辫表示的系列文章中的第一篇。引入一个组合符号，它确定了一个有向的生成表面F的代表L的l。表面F在三维空间中相对于编织轴A和A的补集的纤维化中的纤维处于特殊位置。这个符号同时描述了F作为嵌入面和L作为闭合辫。因此，它在几何和代数上都有意义。在此基础上，引入了一个复杂度函数.证明了当复杂度最小时，l在每个辫群Bn中至多可由200个组合符号描述，从而可由200个共轭类描述。
This paper is the first in a series which study the closed braid representatives of an oriented link type l in oriented 3-space. A combinatorial symbol is introduced which determines an oriented spanning surface F for a representative L of l. The surface F is in a special position in 3-space relative to the braid axis A and fibers in a fibration of the complement of A. The symbol simultaneously describes F as an embedded surface and L as a closed braid. Therefore it is both geometrically and algebraically meaningful. Using it, a complexity function is introduced. It is proved that l is described by at most finitely many combinatorial symbols, and thus by finitely many conjugacy classes in each braid group Bn when the complexity is minimal.