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Sur le groupe fondamental d’un feuilletage. (The fundamental group of a foliation). (French) Zbl 0575.57015
This note is a contribution to recent work on the transverse structure of a foliation [J. Pradines, ibid. 298, 297-300 (1984; Zbl 0568.57018); see also Structure transverse des feuilletages, Toulouse 1982, Astérisque 116 (1984; Zbl 0534.00014)]. The fundamental group \(\pi\) (\({\mathcal F})\) of a foliated manifold (V,\({\mathcal F})\), introduced by W. van Est [ibid. 116, 235-292 (1984; Zbl 0543.58003)] in the abstract framework of manifold schemes, is here considered from a purely geometrical point of view. The canonical epimorphism \(\pi\) (V)\(\to \pi ({\mathcal F})\) is described and also, in case of \({\mathcal F}\) simple, the canonical isomorphism of \(\pi\) (\({\mathcal F})\) with the fundamental group of the space of leaves V/\({\mathcal F}\). A forthcoming paper [Cah. Topologie Géom. Différ. Catégoriques 25, 381-428 (1984)] will include complete proofs.
Reviewer: Reviewer (Berlin)

57R30 Foliations in differential topology; geometric theory
57M05 Fundamental group, presentations, free differential calculus