2005/07/06 by William W. Menasco, Menasco, William W.
Computer Science · Mathematics · #20F36 #57M25 #57M27 #57N35 #Bayesian Methods and Mixture Models #FOS: Mathematics #General Topology (math.GN) #Geometric Topology (math.GT) #math.GN #math.GT #msc:20F36 #msc:57M25 #msc:57M27 #msc:57N35
paper · pdf · doi:10.48550/arxiv.math/0507124
This paper has been withdrawn and replaced by arXiv:math.GT0404602, 26 JAN 2012 which is titled " Recognizing destabilization, exchange moves and flypes"
openalex publication_date 2005/07/06 · arxiv created 2012/01/26 · arxiv updated 2012/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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".