Cohomologie basique et dualité des feuilletages riemanniens
Sergiescu, Vlad
Annales de l'Institut Fourier, Tome 35 (1985), p. 137-158 / Harvested from Numdam
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Nous démontrons des théorèmes de dualité de Poincaré et de de Rham pour la cohomologie basique et l’homologie des courants transverses invariants d’un feuilletage riemannien.

We prove Poincaré and de Rham duality theorems for the base-like cohomology and the homology of transverse invariant currents of complete Riemannian foliations.

@article{AIF_1985__35_3_137_0,
     author = {Sergiescu, Vlad},
     title = {Cohomologie basique et dualit\'e des feuilletages riemanniens},
     journal = {Annales de l'Institut Fourier},
     volume = {35},
     year = {1985},
     pages = {137-158},
     doi = {10.5802/aif.1022},
     mrnumber = {87e:53055},
     zbl = {0563.57012},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AIF_1985__35_3_137_0}
}

Sergiescu, Vlad. Cohomologie basique et dualité des feuilletages riemanniens. Annales de l'Institut Fourier, Tome 35 (1985) pp. 137-158. doi : 10.5802/aif.1022. http://gdmltest.u-ga.fr/item/AIF_1985__35_3_137_0/

[1] V.I. Arnold, Small denominators. I. On maps of the circle onto itself, Izv. Acad. Sci. USSR., Ser. Mat., 25, 1 (1961), 21-86. | Zbl 0152.41905

[2] R. Bott, L. Tu, Differential forms in Algebraic Topology, Graduate texts, n° 82, Springer-Verlag (1982). | MR 83i:57016 | Zbl 0496.55001

[3] G.E. Bredon, Sheaf theory, Mac Graw Hill Series in Higher Math., (1967). | MR 36 #4552 | Zbl 0158.20505

[4] Y. Carriere, Flots riemanniens. Journées S.M.F. sur les structures transverses, Astérisque, 116 (1984). | MR 86m:58125a | Zbl 0548.58033

[5] A. El-Kacimi, V. Sergiescu, G. Hector, La cohomologie basique d'un feuilletage riemannien est de dimension finie, Mathematische Zeitschrift, 118 (1985), 593-599. | Zbl 0536.57013

[6] A. El-Kacimi, G. Hector, Décomposition de Hodge basique pour un feuilletage riemannien, Ann. Inst. Fourier, 36-2 (1986), (à paraître). | Numdam | MR 87m:57029 | Zbl 0586.57015

[7] W. Greub, S. Halperin, R. Vanstone, Connections, curvature and cohomology, Academic Press, (1973-1975).

[8] A. Haefliger, Some remarks on foliations with minimal leaves, Journal. Diff. Geom., 15 (1980), 269-284. | MR 82j:57027 | Zbl 0444.57016

[9] A. Hattori, Spectral sequence in the de Rham cohomology of fiber bundles, J. Fac. Sci. Univ. Tokyo. Sec. I, VIII (1960), 289-331. | MR 23 #A2226 | Zbl 0099.18003

[10] G. Hochshild, J.P. Serre, Cohomology of Lie Algebras, Ann. of. Math., 57 (1953), 591-603. | MR 14,943c | Zbl 0053.01402

[11] F. Kamber, P. Tondeur, Duality for Riemannian foliations, Proc. Symp. Pure Math., 40 (1983). | MR 85e:57030 | Zbl 0523.57019

[12] F. Kamber, P. Tondeur, Foliations and metrics in “Differential Geometry”, Ed. Brooks, Gray, Reinhart, Birkhaüser (1983). | Zbl 0542.53022

[13] P. Molino, Feuilletages transversalement complets et applications, Ann. Ec. Norm. Sup., 10 (1977), 289-307. | Numdam | MR 56 #16649 | Zbl 0368.57007

[14] P. Molino, Géométrie globale des feuilletages riemanniens, Proc. Kon. Nederl. Akad., Ser. A., 1, 85 (1982), 45-76. | MR 84j:53043 | Zbl 0516.57016

[15] P. Molino, Feuilletages riemanniens, Cours de IIIè cycle, Montpellier (1983).

[16] B. Reinhart, Harmonic integrals on foliated manifolds, Am. J. of. Math., (1959), 529-536. | MR 21 #6005 | Zbl 0088.07902

[17] B. Reinhart, Differential geometry of foliations, Ergebnisse der Mathematik, n° 99, Springer-Verlag (1983). | MR 85i:53038 | Zbl 0506.53018

[18] Séminaire H. Cartan, E.N.S., (1954-1955), exp. 3. | Numdam