Symmetries of spatial graphs and Simon invariants

Ryo Nikkuni*, Kouki Taniyama

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


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

Original languageEnglish
Pages (from-to)219-236
Number of pages18
JournalFundamenta Mathematicae
Issue number3
Publication statusPublished - 2009


  • Achiral link
  • Linking number
  • Simon invariant
  • Symmetric spatial graph

ASJC Scopus subject areas

  • Algebra and Number Theory


Dive into the research topics of 'Symmetries of spatial graphs and Simon invariants'. Together they form a unique fingerprint.

Cite this