Roots of 3-manifolds and cobordisms

Details Roots of 3-manifolds and cobordisms Roots of 3-manifolds and cobordisms

2005-04-11

arxiv.org/abs/math/0504223v1

Mathematics

Geometric Topology

11 pages, 3 figures

Scientific paper

Given a set of simplifying moves on 3-manifolds, we apply them to a given 3-manifold M as long as possible. What we get is a root of M. For us, it makes sense to consider three types of moves: compressions along 2-spheres, proper discs and proper annuli having boundary circles in different components of the boundary of M. Our main result is that for the above moves the root of any 3-manifold exists and is unique. The same result remains true if instead of manifolds we apply the moves to 3-cobordisms.

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