A semi-simplicial approach to foliations and their transverse structure. (English) Zbl 0786.57001
This monograph presents a thorough and self-contained exposition of semi- simplicial manifolds, emphasizing the role they play in the classification of foliations. The advantages of this approach are spelled out in the introduction. For example, by incorporating groupoids, manifolds and semi-simplicial spaces into the classification process one is able to treat transverse structures, like holonomy, in a natural way.
Reviewer: S.Jekel (Boston)
MSC:
57-02 | Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes |
57R32 | Classifying spaces for foliations; Gelfand-Fuks cohomology |
57R30 | Foliations in differential topology; geometric theory |
18G30 | Simplicial sets; simplicial objects in a category (MSC2010) |