2007/10/31 by Ryo Nikkuni
Mathematics · #Advanced Combinatorial Mathematics #Combinatorics #Geometric and Algebraic Topology #Graph #Homotopy #Homotopy and Cohomology in Algebraic Topology #Homotopy lifting property #Invariant (physics) #Mathematical physics #Mathematics #Pure mathematics #Vertex (graph theory) #math.GT #msc:57M15 #msc:57M25 #n-connected
paper · pdf · doi:10.1007/s13163-009-0007-x
published as Rev. Mat. Complut. 23 (2010), 1--17 · 16 pages, 13 figures
arxiv created 2008/12/27 · openalex publication_date 2009/11/02 · arxiv updated 2020/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Edge-homotopy and vertex-homotopy are equivalence relations on spatial graphs which are generalizations of Milnor's link-homotopy. Fleming and the author introduced some edge (resp. vertex)-homotopy invariants of spatial graphs by applying the Sato-Levine invariant for the constituent 2-component algebraically split links. In this paper, we construct some new edge (resp. vertex)-homotopy invariants of spatial graphs without any restriction of linking numbers of the constituent 2-component links by applying the generalized Sato-Levine invariant.