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


57R30 Foliations in differential topology; geometric theory
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