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Journal of the London Mathematical Society 2006 73(1):237-251; doi:10.1112/S0024610705022490
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© The London Mathematical Society

Topological Symmetry Groups of Complete Graphs in the 3-Sphere

Erica Flapan, Ramin Naimi and Harry Tamvakis

Department of Mathematics, Pomona College Claremont, CA 91711, USA eflapan{at}pomona.edu
Department of Mathematics, Occidental College Los Angeles, CA 90041, USA rnaimi{at}oxy.edu
Department of Mathematics, Brandeis University MS 050, PO Box 9110, Waltham, MA 02454-9110, USA harryt{at}brandeis.edu

Received 24 April 2004. Revision received 1 May 2005.

The orientation preserving topological symmetry group of a graph embedded in the 3-sphere is the subgroup of the automorphism group of the graph consisting of those automorphisms which can be induced by an orientation preserving homeomorphism of the ambient space. We characterize all possible orientation preserving topological symmetry groups of embeddings of complete graphs in the 3-sphere.


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