2007/12/06 by Mieczysław K. Dąbkowski, Mieczyslaw K. Dabkowski, Makiko Ishiwata +5
Mathematics · #57M25 (Primary) #57M27 (Secondary) #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M25 #msc:57M27
paper · pdf · doi:10.48550/arxiv.0712.0985
41 pages, 34 figures; to appear in JKTR 16(10), December, 2007
arxiv created 2007/12/06 · openalex publication_date 2007/12/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We start a systematic analysis of links up to 5-move equivalence. Our motivation is to develop tools which later can be used to study skein modules based on the skein relation being deformation of a 5-move (in an analogous way as the Kauffman skein module is a deformation of a 2-move, i.e. a crossing change). Our main tools are Jones and Kauffman polynomials and the fundamental group of the 2-fold branch cover of S3 along a link. We use also the fact that a 5-move is a composition of two rational ± (2,2)-moves (i.e. ± 5/2-moves) and rational moves can be analyzed using the group of Fox colorings and its non-abelian version, the Burnside group of a link. One curious observation is that links related by one (2,2)-move are not 5-move equivalent. In particular, we partially classify (up to 5-moves) 3-braids, pretzel and Montesinos links, and links up to 9 crossings.