Spatial Graphs with Local Knots

Details Spatial Graphs with Local Knots Spatial Graphs with Local Knots

2010-10-04

arxiv.org/abs/1010.0479v2

Mathematics

Geometric Topology

20 pages, 3 figures; in v. 2 the proof of Theorem 1 has been clarified, and other minor revisions have been made

Scientific paper

10.1007/s13163-011-0072-9

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 and 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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