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.

This is a major revision of the original article. Theorem 1.4 has been broadened, in that the assumption of no holonomy is no longer required, only that the holonomy action is equicontinuous. Appendices A and B have been removed, and the fundamental results from these Appendices are now contained in the preprint, arXiv:1107.1910v1