zbMATH — the first resource for mathematics

Feuilletages à singularités. (French) Zbl 0584.57016
The author elaborates on and proves the results which he established in a previous note [C. R. Acad. Sci., Paris, Sér. I 298, 27-30 (1984; Zbl 0571.57023)]. He shows with an example that the procedure sketched in the quoted note (by using a Bott type connection to construct infinitesimal holonomy of a leaf of a singular foliation) is not generally correct. In this paper the author defines infinitesimal holonomy of a leaf by making use of locally constant 1-cocycles.
Finally he generalizes to orientable compact singular foliations of codimension 1 a theorem of W. Wu and G. Reeb [Publ. Inst. Math. Univ. Strasbourg 9 (1952; Zbl 0049.126)] on Pfaff’s 1-forms with singularities of center type.
Reviewer: E.Outerelo

57R30 Foliations in differential topology; geometric theory
58A17 Pfaffian systems