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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Topological symmetry groups of graphs in $ 3$-manifolds


Authors: Erica Flapan and Harry Tamvakis
Journal: Proc. Amer. Math. Soc. 141 (2013), 1423-1436
MSC (2010): Primary 57M15, 57M60; Secondary 05C10, 05C25
Published electronically: August 3, 2012
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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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Additional Information

Erica Flapan
Affiliation: Department of Mathematics, Pomona College, Claremont, California 91711
Email: eflapan@pomona.edu

Harry Tamvakis
Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
Email: harryt@math.umd.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11405-4
PII: S 0002-9939(2012)11405-4
Received by editor(s): June 2, 2011
Received by editor(s) in revised form: August 3, 2011
Published electronically: August 3, 2012
Additional Notes: The first author was supported in part by NSF Grant DMS-0905087.
The second author was supported in part by NSF Grant DMS-0901341.
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.