Ordering the braid groups
Ordering the braid groups
复制标题
订购编织组
DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
B. Wiest
中科院分区：
文献类型：
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作者：
R. Fenn;M. T. Greene;D. Rolfsen;C. Rourke;B. Wiest
我们给出了Artin的辫子群Bn是可右赋权的一个明确的几何论证。这种构造是初等的、自然的，并导致了一种新的、有效地可计算的编织规范形式，我们称之为左协调规范形式。在我们的序中为正(分别为负)的辫子的左一致形式在所出现的最小辫子生成元中具有一致的正(分别为负)指数。由此推论，我们的排序与Dehornoy[6]的相同，是用非常不同的方法构造的，我们恢复了Dehornoy的主要定理，即任何辫子都可以用最小生成元中的正指数或负指数来表示，但不能同时使用两者。我们对序的定义与Mosher的范式[13]有很强的联系，这导致了一个算法来判断给定的辫子是正的、平凡的还是负的，它在辫子的长度上是二次的。AMS分类编号初级：20F60、06F15、20F36次级：57M07、57M25
We give an explicit geometric argument that Artin’s braid group Bn is rightorderable. The construction is elementary, natural, and leads to a new, effectively computable, canonical form for braids which we call left-consistent canonical form. The left-consistent form of a braid which is positive (respectively negative) in our order has consistently positive (respectively negative) exponent in the smallest braid generator which occurs. It follows that our ordering is identical to that of Dehornoy [6], constructed by very different means, and we recover Dehornoy’s main theorem that any braid can be put into such a form using either positive or negative exponent in the smallest generator but not both. Our definition of order is strongly connected with Mosher’s normal form [13] and this leads to an algorithm to decide whether a given braid is positive, trivial, or negative which is quadratic in the length of the braid word. AMS Classification numbers Primary: 20F60, 06F15, 20F36 Secondary: 57M07, 57M25