Symmetries of spatial graphs and Simon invariants

Ryo Nikkuni; Kouki Taniyama

doi:10.4064/fm205-3-2

Symmetries of spatial graphs and Simon invariants

Ryo Nikkuni^*, Kouki Taniyama

^*Corresponding author for this work

School of Education

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

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

Original language	English
Pages (from-to)	219-236
Number of pages	18
Journal	Fundamenta Mathematicae
Volume	205
Issue number	3
DOIs	https://doi.org/10.4064/fm205-3-2
Publication status	Published - 2009

Keywords

Achiral link
Linking number
Simon invariant
Symmetric spatial graph

ASJC Scopus subject areas

Algebra and Number Theory

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10.4064/fm205-3-2

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AU - Taniyama, Kouki

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AB - 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

KW - Achiral link

KW - Linking number

KW - Simon invariant

KW - Symmetric spatial graph

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Symmetries of spatial graphs and Simon invariants

Abstract

Keywords

ASJC Scopus subject areas

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