Symmetries of Spatial Graphs and Rational Twists along Spheres and Tori

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