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Pełne teksty:
Warianty tytułu
Abstrakty
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
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
Słowa kluczowe
Tematy
Kategoryzacja MSC:
- 57R32: Classifying spaces for foliations; Gelfand-Fuks cohomology
- 57R30: Foliations; geometric theory
- 57T99: None of the above, but in this section
- 55U10: Simplicial sets and complexes
- 18B40: Groupoids, semigroupoids, semigroups, groups (viewed as categories)
- 57P99: None of the above, but in this section
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
314
Liczba stron
97
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCCXIV
Daty
wydano
1991
otrzymano
1990-11-13
Twórcy
autor
- Institute of Mathematics, Polish Academy of Sciences, Łódź Branch, Narutowicza 56, 90-136 Łódź, Poland
Bibliografia
- [1] G. Andrzejczak, Some characteristic invariants of foliated bundles, Dissertationes Math. 222 (1984).
- [2] G. Andrzejczak, On foliations of semi-simplicial manifolds and their holonomy, preprint MPI Bonn/SFB 84-85.
- [3] G. Andrzejczak, Supplement to: On foliations of semi-simplicial manifolds and their holonomy; the uniqueness, preprint MPI Bonn/SFB 85-27.
- [4] G. Andrzejczak, On foliations of semi-simplicial manifolds and characteristic homomorphisms, preprint MPI Bonn/SFB 85-62.
- [5] G. Andrzejczak, On some sheaf cohomology of semi-simplicial manifolds and their realizations, Dissertationes Math. 278 (1989).
- [6] R. Bott, Lectures on characteristic classes and foliations, in: Lectures on Algebraic and Differential Topology Delivered at the II. ELAM, Lecture Notes in Math. 279, Springer, Berlin 1972, 1-94.
- [7] R. Bott, H. Shulman and J. Stasheff, On the de Rham theory of certain classifying spaces, Adv. in Math. 20 (1976), 43-56.
- [8] C. Camacho and A. L. Neto, Teoria geometrica das folheações, I.M.P.A., Rio de Janeiro 1979.
- [9] T. E. Duchamp, Characteristic invariants of G-foliations, Thesis, Univ. of Illinois, Urbana-Champaign 1976.
- [10] J. L. Dupont, Curvature and Characteristic Classes, Lecture Notes in Math. 640, Springer, Berlin 1978.
- [11] C. Ehresmann, Structures feuilletées. in: Proc. of the 5th Canad. Math. Cong., 1961; Oeuvres complètes, II.2, 563-626.
- [12] W. T. van Est, Rapport sur les S-atlas, in: Structure Transverse des Feuilletages (Toulouse 1982), Astérisque 116, Soc. Math. de France, 1984, 235-292.
- [13] A. Haefliger, Structures feuilletées et cohomologie à valeurs dans un faisceau de groupoï des, Comment. Math. Helv. 32 (1958), 248-329.
- [14] A. Haefliger, Homotopy and integrability, in: Manifolds (Amsterdam 1970), Lecture Notes in Math. 197, Springer, Berlin 1972, 133-163.
- [15] A. Haefliger, Some remarks on foliations with minimal leaves, J. Differential Geom. 15 (1980), 269-284.
- [16] A. Haefliger, Groupoï des d'holonomie et classifiants, in: Structure Transverse des Feuilletages (Toulouse 1982), Astérisque 116, Soc. Math. de France, 1984, 70-97.
- [17] S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, I, Wiley-Interscience Publ., New York 1963.
- [18] H. B. Lawson Jr., The quantitative theory of foliations, CBMS Regional Conf. Ser. in Math. 27, Providence 1977.
- [19] P. Molino, Classe d'Atiyah d'un feuilletage et connexions transverses projetables, C. R. Acad. Sci. Paris Sér. A-B 272 (1971), A779-A781.
- [20] B. L. Reinhart, Differential Geometry of Foliations, Springer, Berlin 1983.
- [21] G. Segal, Classifying spaces and spectral sequences, IHES Publ. Math. 34 (1968), 105-112.
- [22] I. Tamura, Topology of Foliations, Mir, Moscow 1979 (in Russian; transl. from Japanese).
- [23] P. Ver Eecke, Introduction à la théorie des variétés feuilletées, Esquisses Math. 31, Univ. Amiens, 1982.
- [24] P. Ver Eecke, Sur le groupe fondamental d'un feuilletage, Cahiers Topologie Géom. Différentielle 25 (4) (1984), 381-428.
- [25] P. Ver Eecke, Le groupoï de fondamental d'un feuilletage de Stefan, Publ. Sem. Mat. García de Galdeano, Ser. II, 6, Univ. de Zaragoza, 1986.
Języki publikacji
| EN |
Uwagi
1991 Mathematics Subject Classification: Primary 57R30, 57P99; Secondary 57R32, 18B40, 57T99, 55U10.
Identyfikator YADDA
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ISBN
83-85116-22-2
ISSN
0012-3862
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DML-PL
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