On iterated torus knots and transversal knots
On iterated torus knots and transversal knots
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关于迭代环面结和横向结
DOI：
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发表时间：
2000
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：
W. Menasco
一个纽结类型是交换可约的，如果一个任意的封闭n-辫子代表可以通过辫子同位素、交换移动和+/-不稳定的有限序列改变为具有最小辫子指数的封闭辫子。在手稿[J Birman and NC Wrinkle，On transversally simple knots，preprint（1999）]中，S^3的标准接触结构中的一个横结被定义为横截单的，如果它被其拓扑结类型和自链接数刻画为横截合痕。Birman和Wrinkle [同前]的定理2建立了交换约化蕴涵横向简单性。本文的主要结果证明了迭代环面纽结是交换可约的。然后作为推论，迭代环面结是横截简单的。
A knot type is exchange reducible if an arbitrary closed n-braid representative can be changed to a closed braid of minimum braid index by a finite sequence of braid isotopies, exchange moves and +/- destabilizations. In the manuscript [J Birman and NC Wrinkle, On transversally simple knots, preprint (1999)] a transversal knot in the standard contact structure for S^3 is defined to be transversally simple if it is characterized up to transversal isotopy by its topological knot type and its self-linking number. Theorem 2 of Birman and Wrinkle [op cit] establishes that exchange reducibility implies transversally simplicity. The main result in this note, establishes that iterated torus knots are exchange reducible. It then follows as a Corollary that iterated torus knots are transversally simple.