Topological symmetry groups of graphs embedded in the 3-sphere | Zendy

Erica Flapan | Zendy; Ramin Naimi | Zendy; James Pommersheim | Zendy; Harry Tamvakis | Zendy

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Topological symmetry groups of graphs embedded in the 3-sphere

Author(s) -

Erica Flapan,

Ramin Naimi,

James Pommersheim,

Harry Tamvakis

Publication year - 2005

Publication title -

commentarii mathematici helvetici

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.603

H-Index - 46

eISSN - 1420-8946

pISSN - 0010-2571

DOI - 10.4171/cmh/16

Subject(s) - mathematics , symmetry (geometry) , topology (electrical circuits) , combinatorics , pure mathematics , geometry

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 topo- logical 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.

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