Homology classification of spatial graphs by linking numbers and Simon invariants

Reiko Shinjo, Kouki Taniyama

    Research output: Contribution to journalArticle

    8 Citations (Scopus)

    Abstract

    We show that two embeddings f and g of a finite graph G into the 3-space are spatial-graph-homologous if and only if for each subgraph H of G that is homeomorphic to a disjoint union of two circles, the restriction maps f H and g H have the same linking number, and for each subgraph H of G that is homeomorphic to a complete graph K5 or a complete bipartite graph K3,3, the restriction maps f H and g H have the same Simon invariant.

    Original languageEnglish
    Pages (from-to)53-67
    Number of pages15
    JournalTopology and its Applications
    Volume134
    Issue number1
    DOIs
    Publication statusPublished - 2003 Oct 15

    Fingerprint

    Spatial Graph
    Linking number
    Homeomorphic
    Homology
    Subgraph
    Restriction
    Invariant
    Complete Bipartite Graph
    Finite Graph
    Complete Graph
    Disjoint
    Circle
    Union
    If and only if

    Keywords

    • Delta move
    • Finite type invariant
    • Linking number
    • Simon invariant
    • Spatial graph
    • Spatial-graph-homology

    ASJC Scopus subject areas

    • Geometry and Topology

    Cite this

    Homology classification of spatial graphs by linking numbers and Simon invariants. / Shinjo, Reiko; Taniyama, Kouki.

    In: Topology and its Applications, Vol. 134, No. 1, 15.10.2003, p. 53-67.

    Research output: Contribution to journalArticle

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