Quasigeodesic Flows in Hyperbolic Three-Manifolds

TL;DR

This paper demonstrates the existence of many quasigeodesic flows in hyperbolic three-manifolds with nontrivial second homology, using sutured manifold hierarchies and pseudo-Anosov flows.

Contribution

It introduces a method to construct quasigeodesic flows in hyperbolic 3-manifolds leveraging sutured manifold hierarchies and pseudo-Anosov dynamics.

Findings

Existence of many quasigeodesic flows in specified manifolds

Flows are pseudo-Anosov and almost transverse to foliations

Use of sutured manifold hierarchy as a key tool

Abstract

Any closed, oriented, hyperbolic three-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.