On reduction curves and Garside properties of braids
On reduction curves and Garside properties of braids
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关于辫子的还原曲线和Garside特性
DOI：
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发表时间：
2010
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影响因子：
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通讯作者：
J. González
中科院分区：
文献类型：
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作者：
J. González
本文研究了辫子的约化曲线，以及如何利用约化曲线将辫子精确地分解为更简单的辫子，这与Thurston理论给出的分解并不完全对应。然后，我们研究如何循环滑动（这是一种特殊的共轭）影响的正常形式的辫子相对于其组件的正常形式。最后，使用上述方法，我们提供了一个家庭的编织的例子，其滑动电路集（因此，超首脑会议集）具有指数大小相对于股的数量，也相对于规范长度。
In this paper we study the reduction curves of a braid, and how they can be used to decompose the braid into simpler ones in a precise way, which does not correspond exactly to the decomposition given by Thurston theory. Then we study how a cyclic sliding (which is a particular kind of conjugation) affects the normal form of a braid with respect to the normal forms of its components. Finally, using the above methods, we provide the example of a family of braids whose sets of sliding circuits (hence ultra summit sets) have exponential size with respect to the number of strands and also with respect to the canonical length.