Monotonic Simplification and Recognizing Exchange Reducibility
Abstract
The Markov Theorem Without Stabilization (MTWS) (see math.GT/0310279) established the existence of a calculus of braid isotopies that can be used to move between closed braid representatives of a given oriented link type without having to increase the braid index by stabilization. Although the calculus is extensive there are three key isotopies that were identified and analyzed--destabilization, exchange moves and elementary braid preserving flypes. One of the critical open problems left in the wake of the MTWS is the "recognition problem"--determining when a given closed n-braid admits a specified move of the calculus. In this note we give an algorithmic solution to the recognition problem for three isotopies of the MTWS calculus--destabilization, exchange moves and braid preserving flypes. The algorithm is directed by a complexity measure that can be "monotonic simplified" by that application of "elementary moves".
Cite
@article{arxiv.math/0507124,
title = {Monotonic Simplification and Recognizing Exchange Reducibility},
author = {William W. Menasco},
journal= {arXiv preprint arXiv:math/0507124},
year = {2012}
}
Comments
This paper has been withdrawn and replaced by arXiv:math.GT0404602, 26 JAN 2012 which is titled " Recognizing destabilization, exchange moves and flypes"