topological symmetry group, 3-manifold
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.
© 2013 American Mathematical Society
E. Flapan, H. Tamvakis, Topological Symmetry Groups of Graphs in 3-Manifolds, Proceedings of the AMS, Vol 141, No 4, (2013) 1423–1436. doi: 10.1090/S0002-9939-2012-11405-4