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Propriétés géométriques des feuilletages de codimension un liées à la structure transverse. (French) Zbl 0556.57023
Structure transverse des feuilletages, Toulouse 1982, Astérisque 116, 117-133 (1984).
[For the entire collection see Zbl 0534.00014.]
The author continues his study of the structure of the set of closed transversals to a codimension-one foliation. The secant of homotopy is the sub-semigroup of elements of the fundamental group which can be represented by closed transverse curves. The secant of homology is similarly defined. With certain restrictions placed on these algebraic structures, he obtains results about the topological behavior of the leaves of the foliation, in the spirit of the Poincaré-Bendixson theorem.
Reviewer: S.Goodman

MSC:
57R30 Foliations in differential topology; geometric theory