Spatial Graphs with Local Knots

Document Type

Article

Department

Mathematics (Pomona)

Publication Date

2012

Keywords

Spatial graphs, Local knots, Topological symmetry groups, Prime decomposition

Abstract

It is shown that for any locally knotted edge of a 3-connected graph in S 3, there is a ball that contains all of the local knots of that edge which is unique up to an isotopy setwise fixing the graph. This result is applied to the study of topological symmetry groups of graphs embedded in S 3.

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© 2012 Springer-Verlag

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