Mathematical Sciences: Studying Links Via Closed Braids

设L是定向三维球面S_3中的定向链型，L和L分别由n-和m-辫图定义，表示L。研究者主要关心的是如何在没有稳定的情况下在共轭类之间跳跃。这是理解三维空间中有限的(可能是打结的)简单闭合曲线集合如何相互联系所涉及的技术问题之一。

Let L be an oriented link type in the oriented 3-sphere, S3, and let L and L', defined respectively by closed n- and m-braid diagrams, represent L. The investigator is primarily concerned with understanding how it is possible to jump between conjugacy classes without stabilization. This is one of the technical questions involved in understanding how a finite collection of (possibly knotted) simple closed curves in 3-dimensional space can be linked with one another.