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Symmetries of Spatial Graphs and Rational Twists along Spheres and Tori

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Author(s): Toru Ikeda

Journal: Symmetry
ISSN 2073-8994

Volume: 4;
Issue: 1;
Start page: 26;
Date: 2012;
Original page

Keywords: 3-manifold | geometric topology | symmetry | finite group action | spatial graph | rational twist

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.
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