2005/01/29 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.math/0501539
15 pages, 17 figures; this e-print is an English version of the paper which will appear in "Topology of Knots VII" (Proceeding of the Conference Topology of Knots VII, Dec. 23-26, 2004, TWCU), February, 2005, 37-46 (in Japanese)
arxiv created 2005/01/29 · openalex publication_date 2005/01/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We classify 3-braids up to (2,2)-move equivalence and in particular we show how to adjust the Harikae-Nakanishi-Uchida conjecture so it holds for closed 3-braids. As important steps to classify 3-braids up to (2,2)-move equivalence we prove the conjecture for 2-algebraic links and classify (2,2)-equivalence classes for links up to nine crossings. We analyze the behavior of Kei (involutive quandle) associated to a link under (2,2)-moves. We construct Burnside Kei, Q(m,n), and ask the question, motivated by classical Burnside question: for which values of m and n, is Q(m,n) finite?