Characteristic invariants of foliated bundles. (English) Zbl 0267.57012


57R20 Characteristic classes and numbers in differential topology
57R30 Foliations in differential topology; geometric theory
55R10 Fiber bundles in algebraic topology
Full Text: DOI EuDML


[1] Atiyah, M.F.: Complex analytic connections in fibre bundles, Trans. Amer. Math. Soc.85, 181-207 (1957) · Zbl 0078.16002
[2] Baum, P., Bott, R.: On the zeroes of meromorphic vectorfields, Essays On Topology and Related Topics (dedicated to G. De Rham), 1st Ed. Berlin-Heidelberg-New York: Springer 1970
[3] Borel, A.: Compact Clifford-Klein forms of symmetric spaces, Topology2, 111-122 (1963) · Zbl 0116.38603
[4] Bott, R.: A residue formula for holomorphic vector-fields, Differential Geometry1, 311-330 (1967) · Zbl 0179.28801
[5] Bott, R.: On a topological obstruction to integrability, Proc. Symp. Pure Math., Vol.XVI, 127-131 (1970) · Zbl 0206.50501
[6] Bott, R.: Lectures on characteristic classes and foliations, Springer Lecture Notes279 (1972) · Zbl 0241.57010
[7] Bott, R.: On the Lefschetz formula and exotic characteristic classes, Proc. of the Diff. Geom. Conf. Rome (1971) · Zbl 0254.57013
[8] Bott, R., Haefliger, A.: On characteristic classes of ?-foliations, Bull. Amer. Math. Soc., to appear · Zbl 0262.57010
[9] Cartan, H.: Cohomologie réelle d’un espace fibré principal différentiable, Séminaire Cartan, exposés 19 et 20 (1949/50)
[10] Chern, S.S.: Geometry of characteristic classes, Proc. Canad. Math. Congress Halifax (1971), to appear · Zbl 0209.25401
[11] Chern, S.S., Simons, J.: Some cohomology classes in principal fibre bundles and their applications to Riemannian geometry, Proc. Nat. Acad. Sc. USA68, 791-794 (1971) · Zbl 0209.25401
[12] Chern, S.S., Simons, J.: Characteristic forms and transgression I, to appear
[13] Conlon, L.: Transversally parallelizable foliations of codimension two, to appear · Zbl 0302.57009
[14] Gelfand, I.M., Fuks, D.B.: The cohomology of the Lie algebra of tangent vector fields of a smooth manifold, I and II, Funct. Anal.3, 32-52 (1969), and4, 23-32 (1970)
[15] Gelfand, I.M., Fuks, D.B.: The cohomology of the Lie algebra of formal vectorfields, Izv. Akad. Nauk SSR34, 322-337 (1970)
[16] Godbillon, C.: Cohomologies d’algèbres de Lie de champs de vecteurs formels, Séminaire Bourbaki (novembre 1972), exposé 421 · Zbl 0296.17010
[17] Godbillon, C., Vey, J.: Un invariant des feuilletages de codimension un, C. R. Ac. Sc. Paris, t.273, 92-95 (1971) · Zbl 0215.24604
[18] Godement, R.: Théorie des faisceaux, 1st Ed.: Hermann Paris 1958 · Zbl 0080.16201
[19] Greub, W., Halperin, S., Vanstone, R.: Connections, curvature and cohomology, Vo. III, Academic Press, to appear · Zbl 0372.57001
[20] Grothendieck, A.: Sur quelques points d’algèbre homologique, Tohôku Math. J.9, 119-221 (1957) · Zbl 0118.26104
[21] Grothendieck, A., Dieudonné, J.: Eléments de géométrie algébrique, Chap. III, Part 1, Publ. Math. IHES 11 (1961), Part 2, ibid. 17(1963)
[22] Grothendieck, A.: On the De Rham cohomology of algebraic varieties, Publ. Math. IHES29, 95-103 (1966) · Zbl 0145.17602
[23] Grothendieck, A.: Classes de Chern et représentations linéaires des groupes discrets, Six exposés sur la cohomologie des schémas, North Holland, Amsterdam, exp. VIII, 215-305 (1968)
[24] Haefliger, A.: Feuilletages sur les variétés ouvertes, Topology9, 183-194 (1970) · Zbl 0196.26901
[25] Haefliger, A.: Sur les classes caractéristiques des feuilletages, Séminaire Bourbaki (juin 1972), exposé 412
[26] Heitsch, J.L.: Deformations of secondary characteristic classes, Topology, to appear · Zbl 0268.57010
[27] Illusie, L.: Complexe cotangent et déformations, I et II, Lecture Notes in Math. 239 (1971) and 283 (1972) Springer · Zbl 0224.13014
[28] Kamber, F., Tondeur, Ph.: Flat manifolds, Springer Lecture Notes67, 1-53 (1968) · Zbl 0169.55002
[29] Kamber, F., Tondeur, Ph.: Invariant differential operators and cohomology of Lie algebra sheaves, Differentialgeometrie im Grossen, Juli 1969, Berichte aus dem Math. Forschungsinstitut Oberwolfach, Heft 4, Mannheim, 177-230(1971)
[30] Kamber, F., Tondeur, Ph.: Invariant differential Operators and the cohomology of Lie algebra sheaves, Memoirs Amer. Math. Soc.113, 1-125 (1971) · Zbl 0215.52004
[31] Kamber, F., Tondeur, Ph.: Characteristic classes of modules over a sheaf of Lie algebras, Notices Amer. Math. Soc.19, A-401 (February 1972)
[32] Kamber, F., Tondeur, Ph.: Characteristic invariants of foliated bundles, preprint University of Illinois (August 1972)
[33] Kamber, F., Tondeur, Ph.: Derived characteristic classes of foliated bundles, preprint University of Illinois (August 1972)
[34] Kamber, F., Tondeur Ph.: Cohomologie des algèbres de Weil relatives tronquées, C. R. Ac. Sc. Paris, t.276, 459-462 (1973) · Zbl 0247.57004
[35] Kamber, F., Tondeur, Ph.: Algèbres de Weil semi-simpliciales, C. R. Ac. Sc. Paris, t.276, 1177-1179 (1973); Homomorphisme caractéristique d’un fibré principal feuilleté, ibid. t.276, 1407-1410 (1973); Classes caractéristiques dérivées d’un fibré principal feuilleté, ibid. t.276, 1449-1452 (1973)
[36] Katz, N.M., Oda, T.: On the differentiation of De Rham cohomology classes with respect to parameters, J. Math. Kyoto Univ.8-2, 199-213 (1968) · Zbl 0165.54802
[37] Koszul, J.L.: Déformations et connexions localement plates, Ann. Inst. Fourier, Grenoble18, 103-114 (1968) · Zbl 0167.50103
[38] Lehmann, D.: J-homotopie dans les espaces de connexions et classes exotiques de Chern-Simons, C. R. Ac. Sc. Paris, t.275, 835-838 (1972) · Zbl 0242.57010
[39] Lehmann, D.: Classes caractéristiques exotiques et J-connexité des espaces de connexions, to appear
[40] Martinet, J.: Classes caractéristiques des systèmes de Pfaff, to appear
[41] Matsushima, Y.: On Betti numbers of compact locally symmetric Riemannian manifolds, Osaka Math. J.14, 1-20 (1962) · Zbl 0118.38401
[42] Molino, P.: Connexions et G-structures sur les variétés feuilletées, Bull. Soc. Math. France92, 59-63 (1968) · Zbl 0162.53702
[43] Molino, P.: Classes d’Atiyah d’un feuilletage et connexion transverses projetables, C. R. Ac. Sc. Paris, t.272, 779-781 (1971). · Zbl 0211.26701
[44] Molino, P.: Classes caractéristiques et obstructions d’Atiyah pour les fibrés principaux feuilletés, C. R. Ac. Sc. Paris, t.272, 1376-1378 (1971) · Zbl 0212.29003
[45] Molino, P.: Propriétés cohomologiques et propriétés topologiques des feuilletages à connexion transverse projetable, to appear · Zbl 0269.57014
[46] Pasternack, J. S.: Foliations and compact Lie group actions, Comment. Math. Helv.46, 467-477 (1971) · Zbl 0228.57020
[47] Reinhart, B. L.: Foliated manifolds with bundle-like metrics, Ann. of Math.69, 119-132 (1959) · Zbl 0122.16604
[48] Reinhart, B. L.: Harmonic integrals on foliated manifolds, Amer. J. of Math.81, 529-536 (1959) · Zbl 0088.07902
[49] Vaisman, I.: Sur la cohomologie des variétés Riemanniennes feuilletées, C. R. Ac. Paris, t.268, 720-723 (1969) · Zbl 0175.20302
[50] Vaisman, I.: Sur une classe de complexes de cochaines, Math. Ann.194, 35-42 (1971) · Zbl 0216.44902
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.