Topological Molino's theory

TL;DR

This paper generalizes Molino's theory of Riemannian foliations to compact equicontinuous foliated spaces with dense leaves, linking structural local groups to leaf growth and extending previous results.

Contribution

It extends Molino's theory to a broader class of foliated spaces and establishes a connection between structural local groups and leaf growth patterns.

Findings

Structural local groups are associated with compact equicontinuous foliated spaces.

A partial generalization of Carrière and Breuillard-Gelander's results is achieved.

The growth of leaves is related to the properties of the structural local group.

Abstract

Molino's description of Riemannian foliations on compact manifolds is generalized to the setting of compact equicontinuous foliated spaces, in the case where the leaves are dense. In particular, a structural local group is associated to such a foliated space. As an application, we obtain a partial generalization of results by Carri\`ere and Breuillard-Gelander, relating the structural local group to the growth of the leaves.