JournalscmhVol. 80, No. 2pp. 317–354

Topological symmetry groups of graphs embedded in the 3-sphere

  • Erica Flapan

    Pomona College, Claremont, USA
  • Ramin Naimi

    Occidental College, Los Angeles, USA
  • James Pommersheim

    Reed College, Portland, USA
  • Harry Tamvakis

    Brandeis University, Waltham, USA
Topological symmetry groups of graphs embedded in the 3-sphere cover
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Abstract

The topological symmetry group of a graph embedded in the 33-sphere is the group consisting of those automorphisms of the graph which are induced by some homeomorphism of the ambient space. We prove strong restrictions on the groups that can occur as the topological symmetry group of some embedded graph. In addition, we characterize the orientation preserving topological symmetry groups of embedded 33-connected graphs in the 33-sphere.

Cite this article

Erica Flapan, Ramin Naimi, James Pommersheim, Harry Tamvakis, Topological symmetry groups of graphs embedded in the 3-sphere. Comment. Math. Helv. 80 (2005), no. 2, pp. 317–354

DOI 10.4171/CMH/16