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A semi-simplicial approach to foliations and their transverse structure

Seria
Rozprawy Matematyczne tom/nr w serii: 314 wydano: 1991
Zawartość
Warianty tytułu
Abstrakty
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
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
  • 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
bwmeta1.element.zamlynska-d14ca6fe-b76c-4589-a119-345d2407f071
Identyfikatory
ISBN
83-85116-22-2
ISSN
0012-3862
Kolekcja
DML-PL
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