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Some characteristic invariants of foliated bundles

CONTENTSIntroduction......................................................................50. Preliminaries................................................................7 0.1. Foliations.................................................................7 0.2. Foliated bundles....................................................12 0.3. Chern-Weil homomorphism....................................151. Category of RF-bundles.............................................212. Characteristic diagram for RF-bundles......................263....

A semi-simplicial approach to foliations and their transverse structure

CONTENTSIntroduction......................................................................................5I. The category of semi-simplicial manifolds.....................................7I. 1. Semi-simplicial manifolds and semi-simplicial morphisms..........7I. 2. Γ-bundles over ss-manifolds...................................................16I. 3. Morphisms of groupoids..........................................................26I. 4. The fundamental groupoid of an ss-manifold..........................30II....

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