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Wrinkling of smooth mappings. III. Foliations of codimension greater than one. (English) Zbl 0927.58022
The first paper of the authors with the same title is devoted to the foundations of the wrinkling method concerning singularities of smooth maps [Invent. Math. 130, No. 2, 345-369 (1997; Zbl 0896.58010)]. The present paper is devoted to applications of this technique in foliation theory. The authors prove the theorem of regularization of augmented Haefliger structures established by W. P. Thurston [Comment. Math. Helv. 49, 214-231 (1974; Zbl 0295.57013)] and by the authors, with an alternative proof, in [Funkts. Anal. Prilozh. 11, 43-53 (1977; Zbl 0449.57005)]. Moreover, they prove a multiparametric version of the above result.

58K05 Critical points of functions and mappings on manifolds
57R30 Foliations in differential topology; geometric theory
57R32 Classifying spaces for foliations; Gelfand-Fuks cohomology
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