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Topological Symmetry Groups Of Graphs In 3-Manifolds, Erica Flapan, Harry Tamvakis
Topological Symmetry Groups Of Graphs In 3-Manifolds, Erica Flapan, Harry Tamvakis
Pomona Faculty Publications and Research
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 T of some graph in a hyperbolic rational homology 3-sphere such that the topological symmetry group of T is isomorphic to G.