Topological Molino's theory

Jesús A. Álvarez López and Manuel F. Moreira Galicia

Vol. 280 (2016), No. 2, 257–314

DOI: 10.2140/pjm.2016.280.257

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 Carrière and Breuillard–Gelander, relating the structural local group to the growth of the leaves.

Keywords

equicontinuous foliated space, equicontinuous pseudogroup, groupoid, germ, partial map, compact-open topology, local group, local action, growth

Mathematical Subject Classification 2010

Primary: 57R30

Milestones

Received: 22 May 2014

Revised: 9 November 2014

Accepted: 4 June 2015

Published: 28 January 2016