2012/01/26 by William W. Menasco, Menasco, William W.
Computer Science · Mathematics · #20F36 #57M25 #57M27 #57N35 #FOS: Mathematics #General Topology (math.GN) #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Logic, programming, and type systems #math.GN #math.GT #msc:20F36 #msc:57M25 #msc:57M27 #msc:57N35
paper · pdf · doi:10.48550/arxiv.1201.5436
66 pages, 27 figures (some figures use color). This is a replacement for arXiv:math.GT/0507124 titled "Monotonic Simplification and Recognizing Exchange Reducibility", which has been withdrawn
arxiv created 2012/01/26 · openalex publication_date 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) 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 these three key isotopies of the MTWS calculus. The algorithm is "directed" by a complexity measure that can be \em monotonically simplified by the application of "elementary moves".