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Characteristic classes of subfoliations

Luis A. Cordero, X. Masa (1981)

Annales de l'institut Fourier

This paper is devoted to define a characteristic homomorphism for a subfoliation ( F 1 , F 2 ) and to study its relation with the usual characteristic homomorphism for each foliation (as defined by Bott). Moreover, two applications are given: 1) the Yamato’s 2-codimensional foliation is shown to be no homotopic to F 2 in a (1,2)-codimensional subfoliation; 2) an obstruction to the existence of d everywhere independent and transverse infinitesimal transformations of a foliation F 2 is obtained, when F 2 and these...

Characteristic homomorphism for ( F 1 , F 2 ) -foliated bundles over subfoliated manifolds

José Manuel Carballés (1984)

Annales de l'institut Fourier

In this paper a construction of characteristic classes for a subfoliation ( F 1 , F 2 ) is given by using Kamber-Tondeur’s techniques. For this purpose, the notion of ( F 1 , F 2 ) -foliated principal bundle, and the definition of its associated characteristic homomorphism, are introduced. The relation with the characteristic homomorphism of F i -foliated bundles, i = 1 , 2 , the results of Kamber-Tondeur on the cohomology of g - D G -algebras. Finally, Goldman’s results on the restriction of foliated bundles to the leaves of a foliation...

Classifying toposes and foliations

Ieke Moerdijk (1991)

Annales de l'institut Fourier

For any etale topological groupoid G (for example, the holonomy groupoid of a foliation), it is shown that its classifying topos is homotopy equivalent to its classifying space. As an application, we prove that the fundamental group of Haefliger for the (leaf space of) a foliation agrees with the one introduced by Van Est. We also give a new proof of Segal’s theorem on Haefliger’s classifying space B Γ q .

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