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A set of moves for Johansson representation of 3-manifolds

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Vigara R.

Fundamenta Mathematicae

2006

tom 190

nr 1

245-288

A Dehn sphere Σ in a closed 3-manifold M is a 2-sphere immersed in M with only double curve and triple point singularities. The Dehn sphere Σ fills M if it defines a cell decomposition of M. The inverse image in S² of the double curves of Σ is the Johansson diagram of Σ and if Σ fills M it is possible to reconstruct M from the diagram. A Johansson representation of M is the Johansson diagram of a filling Dehn sphere of M. Montesinos proved that every closed 3-manifold has a Johansson representation coming from a nullhomotopic filling Dehn sphere. In this paper a set of moves for Johansson representations of 3-manifolds is given. This set of moves suffices for relating different Johansson representations of the same 3-manifold coming from nullhomotopic filling Dehn spheres. The proof of this result is outlined here.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Vigara R.

1 2006

Wyniki wyszukiwania

A set of moves for Johansson representation of 3-manifolds