Uniform foliations with Reeb components

TL;DR

This paper investigates uniform foliations with Reeb components on 3-manifolds, providing examples and analyzing their behavior, thereby advancing understanding of foliation structures in geometric topology.

Contribution

It introduces new examples of uniform foliations with Reeb components on closed 3-manifolds and studies their properties in a general setting.

Findings

Examples of uniform foliations with Reeb components on infinite fundamental group manifolds.

Results on the behavior of such foliations on general 3-manifolds.

Insights into the structure of foliations with Reeb components.

Abstract

A foliation on a compact manifold is uniform if each pair of leaves of the induced foliation on the universal cover are at finite Hausdorff distance from each other. We study uniform foliations with Reeb components. We give examples of such foliations on a family of closed $3-$manifolds with infinite fundamental group. Furthermore, we prove some results concerning the behavior of a uniform foliation with Reeb components on general $3-$manifolds.