Geodesic
Symmetries of spatial graphs and Simon invariants
Ryo Nikkuni 1   ; Kouki Taniyama 2
1 Department of Mathematics School of Arts and Sciences Tokyo Woman's Christian University 2-6-1 Zempukuji Suginami-ku, Tokyo 167-8585, Japan
2 Department of Mathematics School of Education Waseda University Nishi-Waseda 1-6-1 Shinjuku-ku, Tokyo 169-8050, Japan
Fundamenta Mathematicae, Tome 205 (2009) no. 3, pp. 219-236 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm205-3-2
Keywords: ordered oriented component link sphere said achiral ambient isotopic its mirror image ignoring orientation ordering components kirk livingston showed achiral linking number congruent modulo paper study orientation preserving reversing symmetries component links spatial complete graphs vertices spatial complete bipartite graphs vertices detail determine necessary conditions linking numbers simon invariants links spatial graphs symmetric

Ryo Nikkuni  1   ; Kouki Taniyama  2

1 Department of Mathematics School of Arts and Sciences Tokyo Woman's Christian University 2-6-1 Zempukuji Suginami-ku, Tokyo 167-8585, Japan
2 Department of Mathematics School of Education Waseda University Nishi-Waseda 1-6-1 Shinjuku-ku, Tokyo 169-8050, Japan 
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Ryo Nikkuni; Kouki Taniyama. Symmetries of spatial graphs and Simon invariants. Fundamenta Mathematicae, Tome 205 (2009) no. 3, pp. 219-236. doi: 10.4064/fm205-3-2

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