Symmetries of spatial graphs and Simon invariants

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 the necessary conditions on linking numbers and Simon invariants for such links and spatial graphs to be symmetric.

16 pages, 14 figures

Cited by in corpus (8)

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• Achiral 1-cusped hyperbolic 3-manifolds not coming from amphicheiral null-homologous knot complements
• Topological Symmetry Groups of Möbius Ladders
• Topological symmetry groups and mapping class groups for spatial graphs