zbMATH — the first resource for mathematics

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].

57R30 Foliations in differential topology; geometric theory