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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm205-3-2,
author = {Ryo Nikkuni and Kouki Taniyama},
title = {Symmetries of spatial graphs and Simon invariants},
journal = {Fundamenta Mathematicae},
volume = {205},
year = {2009},
pages = {219-236},
zbl = {1185.57007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm205-3-2}
}
Ryo Nikkuni; Kouki Taniyama. Symmetries of spatial graphs and Simon invariants. Fundamenta Mathematicae, Tome 205 (2009) pp. 219-236. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm205-3-2/