Thin position and planar surfaces for graphs in the 3-sphere

Details Thin position and planar surfaces for graphs in the 3-sphere Thin position and planar surfaces for graphs in the 3-sphere

2008-07-17

arxiv.org/abs/0807.2865v1

Mathematics

Geometric Topology

7 pages, 1 figure

Scientific paper

We show that given a trivalent graph in $S^3$, either the graph complement
contains an essential almost meridional planar surface or thin position for the
graph is also bridge position. This can be viewed as an extension of a theorem
of Thompson to graphs. It follows that any graph complement always contains a
useful planar surface.

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