2023/08/01 by Deepisha Solanki, Solanki, Deepisha
Computer Science · Engineering · #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #graph theory and CDMA systems #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2308.00732
openalex publication_date 2023/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Our main result is a version of Birman's theorem about equivalence of plats, which does not involve stabilization, for the unlink. We introduce the pocket and flip moves, which modify a plat without changing its link type or bridge index. Theorem 1 shows that using the pocket and flip moves, one can simplify any closed n-plat presentation of the unknot to the standard 0-crossing diagram of the unknot, through a sequence of plats of non-increasing bridge index. The theorem readily generalises to the case of the unlink.