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

Atsuhiko Mizusawa, Ryo Nikkuni

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    Abstract

    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
    DOIs
    Publication statusAccepted/In press - 2013 Sep 13

    Fingerprint

    Spatial Graph
    Homotopy
    Equivalence
    Handlebody
    Homology Groups
    Equivalence relation
    Connected Components
    Divisor
    Linking

    Keywords

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

    ASJC Scopus subject areas

    • Geometry and Topology

    Cite this

    A homotopy classification of two-component spatial graphs up to neighborhood equivalence. / Mizusawa, Atsuhiko; Nikkuni, Ryo.

    In: Topology and its Applications, 13.09.2013.

    Research output: Contribution to journalArticle

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