Topological symmetry groups of graphs in 3-manifolds

Flapan, Erica; Tamvakis, Harry

doi:10.1090/S0002-9939-2012-11405-4

Topological symmetry groups of graphs in $3$-manifolds
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by Erica Flapan and Harry Tamvakis PDF

Proc. Amer. Math. Soc. 141 (2013), 1423-1436 Request permission

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 $\Gamma$ of some graph in a hyperbolic rational homology 3-sphere such that the topological symmetry group of $\Gamma$ is isomorphic to $G$.

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