Impacto
Downloads
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. 109147. ISSN 00308730

PDF
472kB 
Official URL: http://msp.org/pjm/1997/1771/pjmv177n1p08p.pdf
Abstract
The authors discuss a class of flows on 3manifolds 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 "npronged singularity'' for some n≥1, n≠2. If only 1pronged singularities occur the flow is called VAnosov; the authors observe, for example, that the geodesic flow of a compact, hyperbolic 2orbifold is VAnosov.
The main theorem is that every closed 3manifold has a singular Anosov flow. The theorem is proved by constructing a certain link L in the 3sphere such that L is a universal branching link, so every closed 3manifold M is a branched cover of the 3sphere branched over L, and L is the set of singular orbits of some VAnosov flow on S3, so the lifted flow is a singular Anosov flow on M.
In the literature, a singular Anosov flow whose npronged singularities always satisfy n≥3 is called pseudoAnosov. The main theorem should be contrasted with the fact that an Anosov or pseudoAnosov flow can only occur on an aspherical 3manifold—an irreducible 3manifold with infinite fundamental group. The literature contains many constructions of Anosov and pseudoAnosov flows, but it remains unknown exactly which aspherical 3manifolds support such flows
Item Type:  Article 

Uncontrolled Keywords:  hyperbolic 2orbifolds; 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