Topological Symmetry Groups of Graphs in 3-Manifolds
Geometric Topology
2011-08-16 v1
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.
Keywords
Cite
@article{arxiv.1108.2880,
title = {Topological Symmetry Groups of Graphs in 3-Manifolds},
author = {Erica Flapan and Harry Tamvakis},
journal= {arXiv preprint arXiv:1108.2880},
year = {2011}
}