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Groupe fondamental de l’espace des feuilles dans les feuilletages sans holonomie. (Fundamental group of the leaf space of foliations without holonomy). (French) Zbl 0714.57016
The author studies $$C^ 2$$-foliations of codimension 1 with trivial holonomy in two cases: nonsingular foliations of noncompact manifolds, singular foliations of closed manifolds. The principal tool is a quotient of $$\pi_ 1M$$- the fundamental group of the leafspace $$\pi_ 1(M/{\mathcal F})$$. Any subgroup of finite type of $$\pi_ 1(M/{\mathcal F})$$ is a free product of abelian free groups. A geometric interpretation of the factors of rank $$\geq 2$$ is given. In particular, the author deduces the absence of exceptional leaves under certain assumptions on $$\pi_ 1M$$ (for example: $$\pi_ 1M$$ is of finite type and has no free nonabelian quotient). These results are applied to the transversely affine foliations.
Reviewer: A.Piatkowski

##### MSC:
 57R30 Foliations in differential topology; geometric theory
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