Topological Symmetry Groups of Graphs Embedded in the 3-Sphere

Authors

Erica Flapan, Pomona CollegeFollow
Ramin Naimi, Occidental College
James Pommersheim, Pomona CollegeFollow
Harry Tamvakis, Brandeis University

Document Type

Article

Department

Mathematics (Pomona)

Publication Date

2005

Keywords

Topological symmetry group, automorphism group, embedded graph, spatial graph, 3-connected graph

Abstract

The topological symmetry group of a graph embedded in the 3-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 3-connected graphs in the 3-sphere.

Rights Information

© 2005 European Mathematical Society

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

DOI

10.4171/CMH/16

Recommended Citation

E. Flapan, R. Naimi, J. Pommersheim, H. Tamvakis, Topological Symmetry Groups of Embedded Graphs in the 3-sphere, Commentarii Mathematici Helvetici, Vol 80, (2005) 317-354. doi: 10.4171/CMH/16