Combinatoire des simplexes sans singularités. (Combining nonsingular simplexes.) (Q1271458)

A new and simpler proof [\textit{F. Lalonde}, Homologie de Shih d'une submersion, Mém. Soc. Math. Fr., Nouv. Sér. 30 (1987; Zbl 0642.57019)] of the Whitehead conjecture [\textit{J. H. C. Whitehead}, Ann. Math., II. Ser. 41, No. 4, 809-824 (1940; Zbl 0025.09203)] has been stated by the author in [Bull. Soc. Math. Fr. 118, No. 1, 1-25 (1990; Zbl 0713.57014)]. The paper under review presents in a unified way both a new proof of the theorem of Lalonde about the homology of embedded simplexes meeting transversally the foliation of a differentiable manifold, and the extension of that theorem to the homology of immersed simplexes.