| Título: | Geodesic flows on hyperbolic orbifolds, and universal orbifolds |
| Autores: | Lozano Imízcoz, María Teresa ; Montesinos Amilibia, José María |
| Tipo de documento: | texto impreso |
| Editorial: | Pacific Journal of Mathematics, 1997 |
| Dimensiones: | application/pdf |
| Nota general: | info:eu-repo/semantics/openAccess |
| Idiomas: | |
| Palabras clave: | Estado = Publicado , Materia = Ciencias: Matemáticas: Geometria algebraica , Tipo = Artículo |
| Resumen: |
The authors discuss a class of flows on 3-manifolds closely related to Anosov flows, which they call singular Anosov flows. These are flows which are Anosov outside of a finite number of periodic "singular orbits'', such that each singular orbit has a Poincaré section on which the first return map has an "n-pronged singularity'' for some n?1, n?2. If only 1-pronged singularities occur the flow is called V-Anosov; the authors observe, for example, that the geodesic flow of a compact, hyperbolic 2-orbifold is V-Anosov. The main theorem is that every closed 3-manifold has a singular Anosov flow. The theorem is proved by constructing a certain link L in the 3-sphere such that L is a universal branching link, so every closed 3-manifold M is a branched cover of the 3-sphere branched over L, and L is the set of singular orbits of some V-Anosov flow on S3, so the lifted flow is a singular Anosov flow on M. In the literature, a singular Anosov flow whose n-pronged singularities always satisfy n?3 is called pseudo-Anosov. The main theorem should be contrasted with the fact that an Anosov or pseudo-Anosov flow can only occur on an aspherical 3-manifold—an irreducible 3-manifold with infinite fundamental group. The literature contains many constructions of Anosov and pseudo-Anosov flows, but it remains unknown exactly which aspherical 3-manifolds support such flows |
| En línea: | https://eprints.ucm.es/id/eprint/22212/1/montesinos56.pdf |
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