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arXiv · 1304.6204

Reeb stability and the Gromov-Hausdorff limits of leaves in compact foliations

Pablo Lessa
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Abstract

We show that the Gromov-Hausdorff limit of a sequence of leaves in a compact foliation is a covering space of the limiting leaf which is no larger than this leaf's holonomy cover. We also show that convergence to such a limit is smooth instead of merely Gromov-Hausdorff. Corollaries include Reeb's local stability theorem, part of Epstein's local structure theorem for foliations by compact leaves, and a continuity theorem of Alvarez and Candel. Several examples are discussed.

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Pablo Lessa. 2013-04-23. Reeb stability and the Gromov-Hausdorff limits of leaves in compact foliations. https://arxiv.org/abs/1304.6204

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