The Chern-Weil Homomorphism of Regular Lie Algebroids

Kubarski, Jan

Publications du Département de mathématiques (Lyon), (1991), p. 1-69 / Harvested from Numdam

Détail

Publié le : 1991-01-01

Bibliographie

[1] Almeida, R. & Molino, P., Suites d'Atiyah et feuilletages transversalement complets, C. R. Acad. Sci. Paris Ser. I Math., 300(1985), 13-15. | MR 778785 | Zbl 0582.57015

[2] Almeida, R. & Molino, P. Suites d'Atiyah, feuilletages et quantification geometrique, Estrait du Séminaire dix Geometrie différentielle. Montpellier, 1984-85. | Zbl 0596.57017

[3] Chern, S. S., Differential Geometry of fiber bundles, Proceedings of the International Congress of Mathematicians, Cambridge, Mass., 1950, Vol.2, 397-411. Amer. Math. Soc., Providence, R. I., 1952. | MR 45432 | Zbl 0049.24201

[4] Coste, A. & Dazord, P. & Weinstein, A., Groupoïdes symplectiques, Publ. Dep. Math. Université de Lyon 1, 2/A (1987). | Numdam | MR 996653 | Zbl 0668.58017

[5] Dazord, P. & Sondaz, D., Varietes de Poisson - Algebroïdes de Lie, Publ. Dep. Math. Universite de Lyon 1, 1/B (1988). | Numdam | MR 1040867

[6] Ehresmann, C., Les connexions infinitésimales dans un espace fibré différentiable, Colloque de topologie (espaces fibres), Bruxelles, 1950, 29-55. Liege 1951. | MR 42768 | Zbl 0054.07201

[7] Est, W. T. Van, Dense imbeddings of Lie groups. II. (I), Proc. Kon. Ned. Acad. v. Wetensch., Amsterdam, 55, Ser.A, 225-274 (1952). | Zbl 0049.30204

[8] Greub, W., Multilinear algebra, Springer-Verlag New York Inc. 1967. | MR 224623 | Zbl 0387.15001

[9] Greub, W. & Halperin, S. & Vanstone, R., Connections, Curvature, and Cohomology Vol. II, Academic Press, New York and London, 1973. | MR 400275 | Zbl 0335.57001

[10] Greub, W. & Halperin, S. & Vanstone, R. Connections, Curvature, and Cohomology Vol. III, Academic Press, New York and London, 1976. | MR 400275 | Zbl 0372.57001

[11] Kamber, F. & Tondeur, Ph., Foliated Bundles and Characteristic Classes, Lectures Notes in Mathematics 493, Springer-Verlag 1975. | MR 402773 | Zbl 0308.57011

[12] Kubarski, J., Exponential mapping for Lie groupoids, Colloq. Math. XLVII (1982), 267-282. | MR 713145 | Zbl 0523.58045

[13] Kubarski, J. Pradines-type groupoids over foliations; cohomology, connections and the Chern-Weil homomorphism, Preprint Nr 2, Institute of Mathematics, Technical University of Łódż, August 1986, | MR 946719

[14] Kubarski, J. Characteristic classes of some Pradines-type groupoids and a generalization of the Bott Vanishing Theorem, Proceedings of the Conference on Differential Geometry and Its Applications, August 24-30, 1986, Brno, Czechoslovakia, Communications, Brno, 1987, 189-198 | MR 923380 | Zbl 0641.57012

[15] Kubarski, J. Pradines-type groupoids, Supplemento ai Rendiconti del Circolo Matematico di Palermo, Serie II, 16(1987), 125-143. | MR 946719 | Zbl 0642.58005

[16] Kubarski, J. Lie algebroid of a principal fibre bundle - three equivalent definitions, Prace Naukowe Politechniki Szczecinskiej, 11 (1988), 123-145. | MR 1129261 | Zbl 0758.55012

[17] Kubarski, J. Same invariants of Lie algebroids of principal fibre bundles, Supplemento ai Rendiconti del Circolo Matematico di Palermo, Serie II, 21(1989), 235-258. | MR 1009576 | Zbl 0678.55011

[18] Kubarski, J. Pontryagin algebra of a transitive Lie algebroid, Supplemento ai Rendiconti del Circolo Matematico di Palermo, Serie II, 22(1989), 117-126. | MR 1061794 | Zbl 0711.55010

[19] Kubarski, J. Lie algebroid of a principal fibre bundle, Publ. Dep. Math.Université de Lyon 1, (to appear). | Numdam | MR 1129261

[20] Kubarski, J. A criterion for the minimal closedness of the Lie subalgebra corresponding to a connected nonclosed Lie subgroup, Revista Matematica de la Universidad Complutense de Madrid (to appear). | MR 1145691 | Zbl 0766.17004

[21] Libermann, P., Sur les prolongements des fibres principaux et les groupoïdes differentiables. Seminaire Analyse Global, Montreal, 1969. | MR 356117 | Zbl 0248.53031

[22] Lisiecki, K., Foliated groupoids, Supplemento ai Rendiconti del Circolo Matematico di Palermo, Serie II, 22(1989), 127-149. | MR 1061795 | Zbl 0707.57016

[23] Mackenzie, K., Lie groupoids and Lie algebroids in differential Geometry, London Mathematical Society Lecture Note Series 124, Cambridge, 1987. | MR 896907 | Zbl 0683.53029

[24] Mackenzie, K. Algebraic constructions in the category of Lie algebroids, J. Algebra (to appear). | MR 1037400 | Zbl 0696.22007

[25] Malcev, A., Subgroups of Lie groups in the large, C. R. (Doklady) Acad. Sci. URSS (N, S.) 36 (1942), 5-7. (Kraus Reprint LTD. VADUZ 1963). | MR 7423 | Zbl 0061.04604

[26] Molino, P., Etude des feuilletages transversalement complets et applications, Ann. Sci. École Norm. Sup., 10(3) (1977), 289-307. | Numdam | MR 458446 | Zbl 0368.57007

[27] Molino, P. Riemannian Foliations, Progress in Mathematics Vol. 73, Birkhäuser Boston Basel, 1988. | MR 932463 | Zbl 0633.53001

[28] Moore, C. C. & Schochet, C., Global Analysis on Foliated Spaces, Mathematical Sciences Research Institute publications; 9. 1988, Springer-Verlag New-York Inc. | MR 918974 | Zbl 0648.58034

[29] Pradines, J., Theorie de Lie pour les groupoïdes differentiates dans la categorie des groupoïdes, Calcul differential dans la categorie des groupoïdes infinitesimaux", C. R. Acad. Sci. Ser.A-B, Paris, 264, (1967), 265-248, [ | MR 216409 | Zbl 0154.21704

[30] Pradines, J. Theorie de Lie pour les groupoïdes differentiables, Atti Conv Intern Geom 7 Diff. Bologna, 1967, Bologna-Amsterdam. | Zbl 0232.22028

[31] Silva, A. M., Atiyah sequences and complete closed pseudogroups preserving a local parallelism. Holomorphic dynamics, Proc. 2nd Int. Colloq. Dyn. Syst., Mexico City/Mex. 1986, Lecture Notes Math. 1345, 302-316 (1988). | MR 980966 | Zbl 0669.58039

[32] Wineerg, E. & Onishchik, A., A seminar on Lie groups and algebraic groups" (in Russian), Moscov, 1988. | Zbl 0722.22004