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

Symmetries of Spatial Graphs and Rational Twists along Spheres and Tori

Toru Ikedaemail
Department of Mathematics, Faculty of Science, Kochi University, 2-5-1 Akebono-cho, Kochi-Shi, Kochi 780-8520, Japan
Received: 14 November 2011; in revised form: 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

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MDPI and ACS Style

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

AMA Style

Ikeda T. Symmetries of Spatial Graphs and Rational Twists along Spheres and Tori. Symmetry. 2012; 4(1):26-38.

Chicago/Turabian Style

Ikeda, Toru. 2012. "Symmetries of Spatial Graphs and Rational Twists along Spheres and Tori." Symmetry 4, no. 1: 26-38.

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