论文标题
卫星结无法由正面的正辫子代表
Satellite knots that cannot be represented by positive braids with full twists
论文作者
论文摘要
众所周知，具有至少一个完整扭曲的正面辫子是最小的辫子，即，它的闭合是辫子指数。在本文中，我们发现打结是闭合正面最小辫子的结，这些辫子不能由带有完整曲折的正辫子代表。更确切地说，我们表明，某些卫星结与同伴和图案，因为闭合辫子不能表示为闭合正面辫子的闭合。结果，我们发现许多卫星结与同伴和模式是不是洛伦兹结的洛伦结。这给出了一个问题，该问题是否具有洛伦兹图案和同伴的卫星结是否也是洛伦兹结，最初是由Birman和Williams在1980年代的一个特殊情况下解决的。
A positive braid with at least one full twist is known to be a minimal braid, i.e, it achieves the braid index for its closure. In this paper we find knots that are the closure of positive minimal braids that cannot be represented by positive braids with full twists. More precisely, we show that some satellite knots with companions and patterns given as the closure of positive braids cannot be represented as the closure of positive braids with full twists. As a consequence, we find infinitely many satellite knots with companions and patterns being Lorenz knots that are not Lorenz knots. This gives an answer to the question whether a satellite knot having Lorenz pattern and companion is also a Lorenz knot, originally addressed by Birman and Williams in a special case in the 1980s.
