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

Symmetries of Spatial Graphs and Rational Twists along Spheres and Tori

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 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 which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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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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