2016/04/28 by Liangxia Wan, Wan, Liangxia
Computer Science · Mathematics · #57M15 #57M27 #Advanced Combinatorial Mathematics #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1604.08386
openalex publication_date 2016/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
New presentations of a link and a virtual link are introduced and algebraic systems on links and virtual links are constructed respectively. Based on the algebraic systems, Reduction Crossing Algorithms for them are proposed which are used to reduce the number of crossings in a link and virtual link. For known unknots, one can transform them into a trivial knot in a polynomial time by applying corresponding algorithm. As special consequences, Goeritz's unknot and Thistlethwaite's unknot are unknotted. Moreover, an infinite family of knots K_G2k,2l are unknotted in O(n2) time where n is the number of crossings in each K_G2k,2l for k,l≥ 0.