CONTENTS Introduction.........................................................................5 I. Semi-simplicial morphisms and topology..........................7 II. Foliated ss-manifolds and sheaf cohomology................13 III. Sheaf cohomology of ss-manifolds...............................32 References.......................................................................55
CONTENTS Introduction......................................................................................5 I. The category of semi-simplicial manifolds.....................................7 I. 1. Semi-simplicial manifolds and semi-simplicial morphisms..........7 I. 2. Γ-bundles over ss-manifolds...................................................16 I. 3. Morphisms of groupoids..........................................................26 I. 4. The fundamental groupoid of an ss-manifold..........................30 II. Foliations of semi-simplicial manifolds........................................41 II. 1. Foliated ss-manifolds.............................................................41 II. 2. Foliations modelled on a pseudogroup..................................51 II. 3. Holonomy and the transverse structure.................................56 II. 4. A relationship with fundamental groups..................................68 II. 5. Foliated bundles and G-structures.........................................79 References....................................................................................92 Index of symbols............................................................................94 Index..............................................................................................96