Bott's vanishing theorem for regular Lie algebroids

Transactions of the American Mathematical Society

Volumn 348, Issue 6, 1996, Pages 2151-2167

  Kubarski, Jan ^a  

^a LODZ UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Bott's phenomenon; Chern Weil homomorphism; Lie algebroid; Nonclosed Lie subgroup; Transversally complete foliation

Indexed keywords

EID: 21344462737     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-96-01646-7     Document Type: Article

References (19)

1. [A] A. Andrzejczak, Some characteristic invariants of foliated bundles, Dissertationes Mathematicae, 222, (1984). MR 85h:57034
2. [A-M] R. Almeida, P.Molino, Suites d'Atiyah et feuilletages transversalement complets, C. R. Acad. Sc. Paris. 300, 1985, Série 1, 13-15. MR 86i:57029
3. [C-D-W] A Coste, P. Dazord, A. Weinstein, Groupoïdes symplectiques, Publ. Dép. Math. Univ. Lyon Ser. A 2 (1987). MR 90g:58033
4. [G] W. Greub, Multilinear algebra, Springer-Verlag, New York, 1967. MR 37:222
5. [G-H-V] W. Greub, S. Halperin, R. Vanstone, Connections, Curvature, and Cohomology. Vols. II, III, Academic Press, New York, 1973, 1976. MR 49:1424, MR 53: 4110
6. [K-T] F. Kamber, Ph. Tondeur, Foliated Bundles and Characteristic Classes, Lectures Notes in Mathematics 493, Springer-Verlag 1975. MR 53:6587
7. [K1] J. Kubarski, Lie algebroid of a principal fibre bundle, Publ. Dépt. Math. Univ. Lyons N. S. A 1989, no. 1, 1-66. MR 92h:58206
8. [K2] _, A criterion for the minimal closedness of the Lie subalgebra corresponding to a connected nonclosed Lie subgroup, Rev. Mat. Univ. Complut. Madrid 4 (1991), 159-176. MR93c:22011
9. [K3] _, The Chern-Weil homomorphism of regular Lie algebroids, Publ. Dépt. Math. Univ. Lyons N.S. A (to appear).
10. [K4] _, Tangential Chern-Weil homomorphism, International Symposium/Workshop on Geometric Study of Foliations, November 15-26 1993, Tokyo (to appear)
11. [L1] P. Libermann, Pseudogroupes infinitésimaux attachés aux pseudogroupes de Lie, Bull. Soc. Math. France, 87, (1959), 409-425. MR 23:A607
12. [L2] _, Sur les prolongements des fibrés principaux et des groupoïdes différentiates banachiques, Seminaire de mathématiques superieures - été 1969, Analyse Globale, Les Presses de l'Université de Montréal, 1971, pp. 7-108. MR 50:8688
13. [MA] K. Mackenzie, Lie groupoids and Lie algebroids in differential, Geometry, London Mathematical Society Lecture Note Series 124, Cambridge, 1987. MR 89g:58225
14. [MO1] P. Molino, Etude des feuilletages transversalement complets et applications, Ann. Sci. Ecole Norm. Sup., (4) 10 (1977), 289-307. MR 56:16649
15. [MO2] _, Riemannian Foliations, Progresss in Mathematics, Vol. 73, Birkhäuser, Boston, Basel, 1988. MR 89b:53054
16. [P] J. Pradines, Théorie de Lie pour les groupoïdes différentiables, Atti Conv. Intern. Geom. 7 Diff. Bologne, 1967, Bologna-Amsterdam.
17. [NVQ] Ngo-Van-Que, Du prolongement des espaces fibrés et des structure infinitésimales, Ann. Inst. Fourier, (Grenoble), 17 (1967), 157-223. MR 36:4468
18. [T1] N. Teleman, Cohomology of Lie algebras, Global Analysis and its Applications, Vol. III, Intern. Course, Trieste 1972, Internat. Atomic Energy Agency, Vienna 1974, pp. 195-202. MR 55:9112
19. [T2] _, A characteristic ring of a Lie algebra extension, Accad. Naz. Lincei. Rend. Cl. Sci. Fis. Mat. Natur. (8), 52 (1972), 498-506 and 708-711, 1972. MR 49:6251