A set of moves for Johansson representation of 3-manifolds

• Autorzy: Rubén Vigara
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 57N35: Embeddings and immersions
• 57N10: Topology of general 3 -manifolds
• 57M99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2006
• Tom: 190
• Numer: 1
• Strony: 245-288

Daty

wydano

2006

Twórcy

autor

Rubén Vigara

• Departamento de Matemáticas Fundamentales, Facultad de Ciencias, U.N.E.D., C/ Senda del rey 9, 28040 Madrid, Spain

Identyfikatory

DOI

10.4064/fm190-0-10