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Holonomy and basic cohomology of foliations

Part of: Differential topology

Published online by Cambridge University Press:  09 April 2009

Peter Y. Pang
Peter Y. Pang
Affiliation:
Department of MathematicsNational University of SingaporeKent Ridge Republic of Singapore 0511 e-mail: [email protected]
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Abstract

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In this paper, we consider the relationship between the cohomologies of the basic differential forms and the transverse holonomy groupoid of a foliation. Applications to minimal models are given.

Keywords

Foliationsbasic cohomologytransverse holonomyminimal models.

MSC classification

Secondary: 57R32: Classifying spaces for foliations; Gelfand-Fuks cohomology
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 60 , Issue 3 , June 1996 , pp. 287 - 300
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Benson, C. and Ellis, D. B., ‘Characteristic classes of transversely homogeneous foliations’, Trans. Amer. Math. Soc. 289 (1985), 849–859.CrossRefGoogle Scholar
[2]Buffet, J.-P. and Lor, J.-C., ‘Une construction d'un universel pour une classe assez large de Γ-structures’, C. R. Acad. Sci. Paris Sér. 1 Math. A 270 (1970), 640–642.Google Scholar
[3]da Silveira, F. E. A., ‘Rational homotopy theory of fibrations’, Pacific J. Math. 113 (1984), 1–34.CrossRefGoogle Scholar
[4]Dupont, J., Curvature and characteristic classes, Lecture Notes in Math. 640 (Springer, Berlin, 1978).CrossRefGoogle Scholar
[5]Kacimi-Alaoui, A. El, Sergiescu, V. and Hector, G., ‘La cohomologie basique d'un feuilletage riemannien est de dimension finie’, Math. Z. 188 (1985), 593–599.CrossRefGoogle Scholar
[6]Greub, W., Halperin, S. and Vanstone, R., Connections, curvature and cohomology, II (Academic Press, New York, 1973).Google Scholar
[7]Griffiths, P. and Morgan, J., Rational homotopy theory and differential forms, Progr. in Math. 16 (Birkhäuser, Boston, 1981).Google Scholar
[8]Grivel, P., ‘Formes différentielles et suites spectrales’, Ann. Inst. Fourier (Grenoble) 29 (1979), 17–37.CrossRefGoogle Scholar
[9]Haefliger, A., ‘Differential cohomology’, in: Differential topology (Liguori Editore, Napoli, 1979) pp. 19–70.Google Scholar
[10]Haefliger, A., ‘Groupoïdes d'holonomie et classifiants’, Astérisque 116 (1984), 70–79.Google Scholar
[11]Halperin, S., Lectures on minimal models, Publ. Internes de l' U.E.R. de Math. Pures et Appl. 111 (Université de Lille I, 1977).Google Scholar
[12]Kamber, F. and Ph., Tondeur, Foliated bundles and characteristic classes, Lecture Notes in Math. 493 (Springer, Berlin, 1975).CrossRefGoogle Scholar
[13]Kamber, F. and ‘Foliations and metrics’, in: Proc. Special Year in Geometry, Maryland (1981–82), Progr. in Math. 32 (Birkhäuser, Boston, 1983) pp. 103–152.Google Scholar
[14]Kamber, F., Hodge-de Rham theory for Riemannian foliations’, Math. Ann. 227 (1987), 415–431.CrossRefGoogle Scholar
[15]Lehmann, D., Modèle minimal relatif des feuilletages, Lecture Notes in Math. 1183 (Springer, Berlin, 1986) pp. 250–258.Google Scholar
[16]Pang, P., ‘Basic dual homotopy invariants of Riemannian foliations’, Trans. Amer. Math. Soc. 322 (1990), 189–199.CrossRefGoogle Scholar
[17]Winkelnkemper, H., ‘The graph of a foliation’, Ann. Global Anal. Geom. 1 (1983), 51–75.CrossRefGoogle Scholar