On the Number of Periodic Points for Expansive Pseudo-Groups

TL;DR

This paper investigates the number of compact leaves in foliations of compact manifolds with expansive holonomy pseudo-groups, establishing finiteness in codimension-one cases and providing examples with a single compact leaf.

Contribution

It proves that in codimension-one, the number of compact leaves is finite and constructs examples with exactly one compact leaf.

Findings

Number of compact leaves is finite in codimension-one cases

Existence of foliations with exactly one compact leaf

Analysis of expansive holonomy pseudo-groups

Abstract

In this work we consider foliations of compact manifolds whose holonomy pseudo-group is expansive, and analyze their number of compact leaves. Our main result is that in the codimension-one case this number is at most finite, and we give examples of such foliations having one compact leaf.