Partially hyperbolic dynamics and 3-manifold topology

TL;DR

This paper explores the topological aspects of partially hyperbolic diffeomorphisms in 3-manifolds, highlighting key obstructions to the existence of Anosov flows based on recent significant results.

Contribution

It provides an exposition of current research linking 3-manifold topology with partially hyperbolic dynamics, emphasizing Margulis and Plante-Thurston's obstructions.

Findings

Topological obstructions prevent certain 3-manifolds from admitting Anosov flows.

The paper illustrates the connection between hyperbolic dynamics and 3-manifold topology.

Recent results clarify the conditions under which Anosov flows can exist.

Abstract

This is an expository note intended to illustrate current research in topological study of partially hyperbolic diffeomorphisms in dimension 3 with a beautiful result due to Margulis and Plante-Thurston on topological obstructions for a manifold to admit an Anosov flow.