A set of moves for Johansson representation of 3-manifolds

Rubén Vigara

Fundamenta Mathematicae (2006)

  • Volume: 190, Issue: 1, page 245-288
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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Rubén Vigara. "A set of moves for Johansson representation of 3-manifolds." Fundamenta Mathematicae 190.1 (2006): 245-288. <http://eudml.org/doc/282588>.

@article{RubénVigara2006,
abstract = {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.},
author = {Rubén Vigara},
journal = {Fundamenta Mathematicae},
keywords = {Dehn surface; Johansson diagram},
language = {eng},
number = {1},
pages = {245-288},
title = {A set of moves for Johansson representation of 3-manifolds},
url = {http://eudml.org/doc/282588},
volume = {190},
year = {2006},
}

TY - JOUR
AU - Rubén Vigara
TI - A set of moves for Johansson representation of 3-manifolds
JO - Fundamenta Mathematicae
PY - 2006
VL - 190
IS - 1
SP - 245
EP - 288
AB - 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.
LA - eng
KW - Dehn surface; Johansson diagram
UR - http://eudml.org/doc/282588
ER -

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