Roots in 3-manifold topology
Geometric Topology
2009-04-10 v1
Abstract
Let C be some class of objects equipped with a set of simplifying moves. When we apply these to a given object M in C as long as possible, we get a root of M. Our main result is that under certain conditions the root of any object exists and is unique. We apply this result to different situations and get several new results and new proofs of known results. Among them there are a new proof of the Kneser-Milnor prime decomposition theorem for 3-manifolds and different versions of this theorem for cobordisms, knotted graphs, and orbifolds.
Cite
@article{arxiv.0904.1531,
title = {Roots in 3-manifold topology},
author = {Cynthia Hog-Angeloni and Sergei Matveev},
journal= {arXiv preprint arXiv:0904.1531},
year = {2009}
}
Comments
This is the version published by Geometry & Topology Monographs on 29 April 2008