Symmetries of spatial graphs and Simon invariants
Tom 205 / 2009
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.