Homogeneous matchbox manifolds

Abstract

We prove that a homogeneous matchbox manifold of any finite dimension is homeomorphic to a McCord solenoid, thereby proving a strong version of a conjecture of Fokkink and Oversteegen. The proof uses techniques from the theory of foliations that involve making important connections between homogeneity and equicontinuity. The results provide a framework for the study of equicontinuous minimal sets of foliations that have the structure of a matchbox manifold.