Homogeneous matchbox manifolds

Alex Clark; Steven Hurder

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arXiv · 1006.5482

Homogeneous matchbox manifolds

Alex Clark·Steven Hurder

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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.

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Alex Clark, Steven Hurder. 2010-06-28. Homogeneous matchbox manifolds. https://arxiv.org/abs/1006.5482

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