Symmetries of spatial graphs and Simon invariants

Ryo Nikkuni; Kouki Taniyama

Symmetries of spatial graphs and Simon invariants

Ryo Nikkuni; Kouki Taniyama

Fundamenta Mathematicae (2009)

Volume: 205, Issue: 3, page 219-236
ISSN: 0016-2736

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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.

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Ryo Nikkuni, and Kouki Taniyama. "Symmetries of spatial graphs and Simon invariants." Fundamenta Mathematicae 205.3 (2009): 219-236. <http://eudml.org/doc/282642>.

@article{RyoNikkuni2009,
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.},
author = {Ryo Nikkuni, Kouki Taniyama},
journal = {Fundamenta Mathematicae},
keywords = {achiral link; Simon invariant; symmetric spatial graph; linking number},
language = {eng},
number = {3},
pages = {219-236},
title = {Symmetries of spatial graphs and Simon invariants},
url = {http://eudml.org/doc/282642},
volume = {205},
year = {2009},
}

TY - JOUR
AU - Ryo Nikkuni
AU - Kouki Taniyama
TI - Symmetries of spatial graphs and Simon invariants
JO - Fundamenta Mathematicae
PY - 2009
VL - 205
IS - 3
SP - 219
EP - 236
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.
LA - eng
KW - achiral link; Simon invariant; symmetric spatial graph; linking number
UR - http://eudml.org/doc/282642
ER -

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