Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-11T07:33:50.210Z Has data issue: false hasContentIssue false

Compressible ends of leaves in foliated 3-manifolds

Published online by Cambridge University Press:  09 April 2009

Charalambos Charitos
Affiliation:
Agricultural University of Athens Department of Mathematics 75 Iera Odos, 118 55 AthensGreece e-mail: gmat2xax@auadec.aua.ariadne-t.gr
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we study the asymptotic behavior of cylindrical ends in compact foliated 3-manifolds and give a sufficient condition for these ends to spiral onto a toral leaf.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1997

References

[C-C1]Cantwell, J. and Conlon, L.Poincaré-Bendixson theory for leaves of condimension one’, Trans. Amer. Math. Soc. (1981), 181209.Google Scholar
[C-C2]Cantwell, J. and Conlon, L., ‘Leaves with isolated ends in foliated 3-manifolds’, Topology 16 (1972), 311322.CrossRefGoogle Scholar
[G]Godbillon, C., Théorie géométrique des feuilletages (Birkhäuser, Boston, 1992)Google Scholar
[H]Hector, G., ‘Feuilletages en cylindres’, in: Lecture Notes in Math. 597 (Springer, Berlin, 1977) pp. 252270.Google Scholar
[N]Novikov, S. P., ‘Topology of foliations’, Trans. Moscow Math. Soc. (1965), 268304.Google Scholar
[Ni]Nishimori, T., ‘Isolated ends of open leaves of codimension one foliations’, Quart. J. Math. Oxford 26 (1975), 159167.CrossRefGoogle Scholar
[Ro]Rolfsen, D., Knots and links (Publish or Perish, Inc., Houston, 1976).Google Scholar
[R-R]Rosenberg, H. and Roussarie, R., ‘Reeb foliations’, Ann. of Math. 91 (1970), 124.CrossRefGoogle Scholar