Braid ordering and the geometry of closed braid
Braid ordering and the geometry of closed braid
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DOI：
10.2140/gt.2011.15.473
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发表时间：
2008-05
影响因子：
2
通讯作者：
Tetsuya Ito
中科院分区：
文献类型：
--
作者：
Tetsuya Ito
研究了辫群的Dehornoy序与闭辫补的拓扑和几何之间的关系。我们表明，Dehornoy地板的辫子，这是一个非负整数确定的Dehornoy顺序，告诉我们的位置本质表面的封闭辫子补充。进一步证明了如果辫子的Dehornoy底大于或等于2，则辫子的Nielsen-Thurston分类与闭辫子补的几何结构是一一对应的. 57 M25; 57 M50
We study the relationships between the Dehornoy ordering of the braid groups and the topology and geometry of the closed braid complements. We show that the Dehornoy floor of braids, which is a nonnegative integer determined by the Dehornoy ordering, tells us the position of essential surfaces in the closed braid complements. Furthermore, we prove that if the Dehornoy floor of a braid is bigger than or equal to two, then the Nielsen‐Thurston classification of braids and the geometric structure of the closed braid complements are in one-to-one correspondence. 57M25; 57M50