Resilient leaves in transversely affine foliations (Q1121560)
From MaRDI portal
| This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Resilient leaves in transversely affine foliations |
scientific article; zbMATH DE number 4104003
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Resilient leaves in transversely affine foliations |
scientific article; zbMATH DE number 4104003 |
Statements
Resilient leaves in transversely affine foliations (English)
0 references
1989
0 references
\textit{P. Furness} and \textit{E. Fedida} [Glasg. Math. J. 17, 106-111 (1976; Zbl 0329.57004), Theorem 3] incorrectly asserted that a transversely affine foliation of codimension one cannot have exceptional leaves. In this paper a counterexample to their assertion is given on a closed 3- manifold. (It seems that a similar example was already known to \textit{G. Hector} (unpublished).) It is also shown that a transversely affine foliation of codimension one has locally dense resilient leaves if and only if its global holonomy group is non-abelian. This result contains Theorem 1 of \textit{P. Furness} and \textit{E. Fedida} [C. R. Acad. Sci. Paris, Ser. A 282, 825-827 (1976; Zbl 0321.57017)] as a special case.
0 references
transversely affine foliation of codimension one
0 references
exceptional leaves
0 references
locally dense resilient leaves
0 references
global holonomy group
0 references