Roots of knotted graphs and orbifolds

Details Roots of knotted graphs and orbifolds Roots of knotted graphs and orbifolds

2005-04-20

arxiv.org/abs/math/0504415v1

Mathematics

Geometric Topology

15 pages, 3 figures

Scientific paper

Let G be a graph in a 3-manifold M. We compress the pair (M,G) along
admissible 2-spheres as long as possible. What we get is a root of (M,G). Our
main result is that for any pair (M,G) the root exists and is unique. As a
corollary we get an easy proof of Petronio's theorem on prime decompositions of
3-orbifolds.

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