Structure of equicontinuous foliated spaces

Abstract

Este trabajo trata sobre espacios foliados equicontinuos, considerados como generalizaciones de las foliaciones riemannianas introducidas por Reinhart [40]. Especialmente, se consideran espacios foliados equicontinuos compactos que son minimales en el sentido de que sus hojas son densas.The main goal of this thesis is to prove the structural theorems of Molino’s theory of Riemannian foliations in the topological context; in other words, for compact equicontinuous foliated spaces. This is achieved for the case where the leaves are dense (minimal foliated space), describing such foliated space in terms of a foliated space whose transverse dynamics is given by local left translations in a local group G (a G-foliated space). Then this description is used to study the growth of the leaves in the spirit of Carriére and Breuillard- Gelander.