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Symmetries of spatial graphs and Simon invariants

Tom 205 / 2009

Ryo Nikkuni, Kouki Taniyama Fundamenta Mathematicae 205 (2009), 219-236 MSC: Primary 57M15; Secondary 57M25. DOI: 10.4064/fm205-3-2

Streszczenie

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.

Autorzy

  • Ryo NikkuniDepartment of Mathematics
    School of Arts and Sciences
    Tokyo Woman's Christian University
    2-6-1 Zempukuji
    Suginami-ku, Tokyo 167-8585, Japan
    e-mail
  • Kouki TaniyamaDepartment of Mathematics
    School of Education
    Waseda University
    Nishi-Waseda 1-6-1
    Shinjuku-ku, Tokyo 169-8050, Japan
    e-mail

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