2012/12/31 by Atsuhiko Mizusawa, Ryo Nikkuni · 6 citations
Mathematics · #Advanced Combinatorial Mathematics #Combinatorics #Component (thermodynamics) #Connected component #Discrete mathematics #Equivalence (formal languages) #Geometric and Algebraic Topology #Homotopy #Homotopy and Cohomology in Algebraic Topology #Homotopy category #Homotopy group #Homotopy sphere #Mathematics #Pure mathematics #math.GT #msc:57M15 #msc:57M25 #n-connected
paper · pdf · doi:10.1016/j.topol.2015.05.041
published in Topology and its Applications 196, 710-718 (Elsevier BV) · 10 pages, 11 figures
arxiv created 2015/05/25 · openalex publication_date 2015/05/28 · arxiv updated 2020/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A neighborhood homotopy is an equivalence relation on spatial graphs which is generated by crossing changes on the same component and neighborhood equivalence. We give a complete classification of all 2-component spatial graphs up to neighborhood homotopy by the elementary divisor of a linking matrix with respect to the first homology group of each of the connected components. This also leads a kind of homotopy classification of 2-component handlebody-links.