Geodesic flows on hyperbolic orbifolds, and universal orbifolds



Downloads per month over past year

Lozano Imízcoz, María Teresa and Montesinos Amilibia, José María (1997) Geodesic flows on hyperbolic orbifolds, and universal orbifolds. Pacific Journal of Mathematics, 177 (1). pp. 109-147. ISSN 0030-8730

[thumbnail of montesinos56.pdf]

Official URL:


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

Item Type:Article
Uncontrolled Keywords:hyperbolic 2-orbifolds; branched coverings; singular Anosov flows
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:22212
Deposited On:05 Jul 2013 15:20
Last Modified:12 Dec 2018 15:13

Origin of downloads

Repository Staff Only: item control page