A homotopy classification of two-component spatial graphs up to neighborhood equivalence

Atsuhiko Mizusawa, Ryo Nikkuni

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    1 Citation (Scopus)


    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.

    Original languageEnglish
    JournalTopology and its Applications
    Publication statusAccepted/In press - 2013 Sep 13



    • Delta move
    • Handlebody-link
    • Linking number
    • Spatial graph

    ASJC Scopus subject areas

    • Geometry and Topology

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