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On some sheaf cohomology of semi-simplicial manifolds and their realizations

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Andrzejczak G.

Instytut Matematyczny Polskiej Akademii Nauk

EN

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

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A semi-simplicial approach to foliations and their transverse structure

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Andrzejczak G.

Instytut Matematyczny Polskiej Akademii Nauk

EN

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

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Some characteristic invariants of foliated bundles

100%

Andrzejczak G.

Instytut Matematyczny Polskiej Akademii Nauk

EN

CONTENTS Introduction......................................................................5 0. Preliminaries................................................................7 0.1. Foliations.................................................................7 0.2. Foliated bundles....................................................12 0.3. Chern-Weil homomorphism....................................15 1. Category of RF-bundles.............................................21 2. Characteristic diagram for RF-bundles......................26 3. Pontrjagin classes of foliations...................................40 4. Relative Pontrjagin classes of foliations.....................53 References....................................................................66

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Characteristic classes of foliations preserved by a transverse k-field.

96%

Andrzejczak G.

Banach Center Publications

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1984

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tom 12

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nr 1

23-27

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More characteristic invariants of foliated bundles

84%

Andrzejczak G.

Banach Center Publications

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1984

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tom 12

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nr 1

9-22

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On regular tangent covectors, regular differential forms, and smooth vector fields on a differential space

60%

Andrzejczak G.

Colloquium Mathematicum

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1982

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tom 46

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nr 2

243-255

Ograniczanie wyników

2 Banach Center Publications

1 Colloquium Mathematicum

6 Andrzejczak G.

1 1991

1 1989

3 1984

1 1982

On some sheaf cohomology of semi-simplicial manifolds and their realizations

A semi-simplicial approach to foliations and their transverse structure

Some characteristic invariants of foliated bundles

Characteristic classes of foliations preserved by a transverse k-field.

More characteristic invariants of foliated bundles

On regular tangent covectors, regular differential forms, and smooth vector fields on a differential space