Topological symmetry groups and mapping class groups for spatial graphs

2011/11/11 by Cho, Sangbum, Koda, Yuya · 2 citations
#05C10 (Primary) 57M25 #05C25 #57M15 #57S05 (Secondary) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1111.2668

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.

Cited by

• Handlebody-knots obtained by tangle replacement
• On symmetry and exterior problems of knotted handlebodies

Related

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