Topological symmetry groups and mapping class groups for spatial graphs

Abstract

We give a necessary and sufficient condition for the mapping class group of the pair of the 3-sphere and a graph embedded in it to be isomorphic to the topological symmetry group of the embedded graph.

11 pages, 3 figures; minor changes, typos corrected; to appear in Michigan Mathematical Journal

References in corpus (2)

• Automorphisms of the 3-sphere that preserve spatial graphs and handlebody-knots
• Topological Symmetry Groups of Graphs in 3-Manifolds