Roots in 3-manifold topology

Details Roots in 3-manifold topology Roots in 3-manifold topology

2009-04-09

arxiv.org/abs/0904.1531v1

Geom. Topol. Monogr. 14 (2008) 295-319

Mathematics

Geometric Topology

This is the version published by Geometry & Topology Monographs on 29 April 2008

Scientific paper

10.2140/gtm.2008.14.295

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.

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