English

Roots of knotted graphs and orbifolds

Geometric Topology 2007-05-23 v1

Abstract

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.

Keywords

Cite

@article{arxiv.math/0504415,
  title  = {Roots of knotted graphs and orbifolds},
  author = {Sergei Matveev},
  journal= {arXiv preprint arXiv:math/0504415},
  year   = {2007}
}

Comments

15 pages, 3 figures

R2 v1 2026-07-22T17:18:21.808Z