Topological Symmetry Groups of Graphs in 3-Manifolds

2011/08/14 by Erica Flapan, Flapan, Erica, Harry Tamvakis +1
Mathematics · #05C10 #05C25 #57M15 #57M60 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:05C10 #msc:05C25 #msc:57M15 #msc:57M60

paper · pdf · doi:10.48550/arxiv.1108.2880

arxiv created 2011/08/14 · arxiv updated 2011/08/16

Abstract

We prove that for every closed, connected, orientable, irreducible 3-manifold, there exists an alternating group A_n which is not the topological symmetry group of any graph embedded in the manifold. We also show that for every finite group G, there is an embedding Γ of some graph in a hyperbolic rational homology 3-sphere such that the topological symmetry group of Γ is isomorphic to G.

Related

• Topological symmetry groups and mapping class groups for spatial graphs
• Topological Symmetry Groups of the Generalized Petersen Graphs
• Topological Symmetry Groups of the Heawood Graph
• Topological Symmetry Groups of the Petersen Graph
• Topological Symmetries of the Heawood family