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Endsets of exceptional leaves: A theorem of G. Duminy. (English) Zbl 1011.57009
Walczak, Paweł(ed.) et al., Foliations: geometry and dynamics. Proceedings of the Euroworkshop, Warsaw, Poland, May 29-June 9, 2000. Singapore: World Scientific. 225-261 (2002).
Authors abstract: In 1977 Gerard Duminy proved that, if $$F$$ is a semiproper leaf of a $$C^{2}$$ codimension one foliation $$\mathcal{F}$$ of a compact $$n$$-manifold $$M$$ and $$X$$ is an exceptional local minimal set of $$\mathcal{F}$$, then the set $$\mathcal{E}^{X}\left( F\right)$$ of ends of $$F$$ asymptotic to $$X,$$ if nonempty, is homeomorphic to a Cantor set. No proof of this remarkable result has ever appeared, even in preprint form. Here, we offer a proof of our own.
For the entire collection see [Zbl 0988.00069].

##### MSC:
 57R30 Foliations in differential topology; geometric theory