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Symmetry 2012, 4(1), 26-38; doi:10.3390/sym4010026

Symmetries of Spatial Graphs and Rational Twists along Spheres and Tori

Department of Mathematics, Faculty of Science, Kochi University, 2-5-1 Akebono-cho, Kochi-Shi, Kochi 780-8520, Japan
Received: 14 November 2011 / Revised: 12 January 2012 / Accepted: 13 January 2012 / Published: 20 January 2012
(This article belongs to the Special Issue Symmetry and Beauty of Knots)
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Abstract

A symmetry group of a spatial graph Γ in S3 is a finite group consisting of orientation-preserving self-diffeomorphisms of S3 which leave Γ setwise invariant. In this paper, we show that in many cases symmetry groups of Γ which agree on a regular neighborhood of Γ are equivalent up to conjugate by rational twists along incompressible spheres and tori in the exterior of Γ.
Keywords: 3-manifold; geometric topology; symmetry; finite group action; spatial graph; rational twist 3-manifold; geometric topology; symmetry; finite group action; spatial graph; rational twist
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Ikeda, T. Symmetries of Spatial Graphs and Rational Twists along Spheres and Tori. Symmetry 2012, 4, 26-38.

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