Symmetries of spatial graphs and Simon invariants

Ryo Nikkuni, Kouki Taniyama

    Research output: Contribution to journalArticle

    9 Citations (Scopus)

    Abstract

    An ordered and oriented 2-component link L in the 3-sphere is said to be achiral if it is ambient isotopic to its mirror image ignoring the orientation and ordering of the components. Kirk-Livingston showed that if L is achiral then the linking number of L is not congruent to 2 modulo 4. In this paper we study orientation-preserving or reversing symmetries of 2-component links, spatial complete graphs on 5 vertices and spatial complete bipartite graphs on 3 + 3 vertices in detail, and determine necessary conditions on linking numbers and Simon invariants for such links and spatial graphs to be symmetric

    Original languageEnglish
    Pages (from-to)219-236
    Number of pages18
    JournalFundamenta Mathematicae
    Volume205
    Issue number3
    DOIs
    Publication statusPublished - 2009

    Fingerprint

    Spatial Graph
    Linking number
    Symmetry
    Invariant
    Complete Bipartite Graph
    Congruent
    Complete Graph
    Modulo
    Mirror
    Necessary Conditions

    Keywords

    • Achiral link
    • Linking number
    • Simon invariant
    • Symmetric spatial graph

    ASJC Scopus subject areas

    • Algebra and Number Theory

    Cite this

    Symmetries of spatial graphs and Simon invariants. / Nikkuni, Ryo; Taniyama, Kouki.

    In: Fundamenta Mathematicae, Vol. 205, No. 3, 2009, p. 219-236.

    Research output: Contribution to journalArticle

    Nikkuni, Ryo ; Taniyama, Kouki. / Symmetries of spatial graphs and Simon invariants. In: Fundamenta Mathematicae. 2009 ; Vol. 205, No. 3. pp. 219-236.
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