Homogeneous matchbox manifolds

Details Homogeneous matchbox manifolds Homogeneous matchbox manifolds

2010-06-28

arxiv.org/abs/1006.5482v2

Mathematics

Dynamical Systems

This is a major revision of the original article. Theorem 1.4 has been broadened, in that the assumption of no holonomy is no

Scientific paper

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.

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