Abstract
In this article we prove that any closed, oriented, hyperbolic 3-manifold with nontrivial second homology has many quasigeodesic flows, where quasigeodesic means that flow lines are uniformly efficient in measuring distance in relative homotopy classes. The flows are pseudo-Anosov flows which are almost transverse to finite depth foliations in the manifold. The main tool is the use of a sutured manifold hierarchy which has good geometric properties.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 503-537 |
| Number of pages | 35 |
| Journal | Topology |
| Volume | 40 |
| Issue number | 3 |
| DOIs | |
| State | Published - May 2001 |
All Science Journal Classification (ASJC) codes
- Geometry and Topology
Keywords
- Almost transversality
- Finite depth foliations
- Gromov hyperbolic groups
- Hausdorff leaf space
- Pseudo-Anosov flows
- Quasi-isometries
- Quasigeodesics
- Sutured manifold hierarchies