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.
