The Characteristic Classes of Flat and of Partially Flat Regular Lie Algebroids over Foliated Manifolds

Jan Kubarski

Publications du Département de mathématiques (Lyon) (1994)

  • Issue: 2, page 7-126
  • ISSN: 0076-1656

How to cite

top

Kubarski, Jan. "The Characteristic Classes of Flat and of Partially Flat Regular Lie Algebroids over Foliated Manifolds." Publications du Département de mathématiques (Lyon) (1994): 7-126. <http://eudml.org/doc/273569>.

@article{Kubarski1994,
author = {Kubarski, Jan},
journal = {Publications du Département de mathématiques (Lyon)},
language = {eng},
number = {2},
pages = {7-126},
publisher = {Université Claude Bernard - Lyon 1},
title = {The Characteristic Classes of Flat and of Partially Flat Regular Lie Algebroids over Foliated Manifolds},
url = {http://eudml.org/doc/273569},
year = {1994},
}

TY - JOUR
AU - Kubarski, Jan
TI - The Characteristic Classes of Flat and of Partially Flat Regular Lie Algebroids over Foliated Manifolds
JO - Publications du Département de mathématiques (Lyon)
PY - 1994
PB - Université Claude Bernard - Lyon 1
IS - 2
SP - 7
EP - 126
LA - eng
UR - http://eudml.org/doc/273569
ER -

References

top
  1. [1] Andrzejczak, G., Some characteristic invariants of foliated bundles, Dissertationes Mathematicae, CCXXII, PWNWarszawa1984. Zbl0561.57016MR735920
  2. [2] Andrzejczak, G. - Homomorfizm Cherna-Weila i klasy charakterystyczne foliacji (The Chern-Weil homomorphism and characteristic classes of foliations), refere on The Congress of Polish Society of Mathematics, Czestochowa, September, 1987. 
  3. [3] Almeida, R. & Molino, P., Suites d'Atiyah et feuilletages transversalement complets, C. R. Acad. Sci. Paris Ser. I Math., 300 (1985), 13-15. Zbl0582.57015MR778785
  4. [4] Almeida, R. & Molino, P.Suites d'Atiyah, feuilletages et quantification geometrique, Estrait du Seminaire du Geometrie differentielle, Montpellier, 1984-85. Zbl0596.57017
  5. [5] Coste, A. & Dazord, P. & Weinstein, A., Groupoides symplectiques, Publ. Dep. Math.Universite de Lyon 1, 2/A (1987). Zbl0668.58017MR996653
  6. [6] Ehresmann, C., Les connexions infinitésimales dans un espace fibré différentiable, Colloque de topologie (espaces fibres), Bruxelles, 1950, 29-55. Liege1951. Zbl0054.07201MR42768
  7. [7] Greub, W., Multilinear algebra, Springer-VerlagNew York Inc. 1967. Zbl0387.15001MR224623
  8. [8] Greub, W. & Halperin, S. & Vanstone, R., Connections, Curvature, and Cohomology Vol. II, Academic Press, New York and London, 1973. Zbl0335.57001MR400275
  9. [9] Greub, W. & Halperin, S. & Vanstone, R.Connections, Curvature, and Cohomology Vol. III, Academic Press, New York and London, 1976. Zbl0372.57001MR400275
  10. [10] Kamber, F. & Tondeur, PH., Foliated Bundles and Characteristic Classes, Lectures Notes in Mathematics493, Springer-Verlag1975. Zbl0308.57011MR402773
  11. [11] Kubarski, J., Exponential mapping for Lie groupoids, Colloq. Math.XLVII (1982), 267-282. Zbl0523.58045MR713145
  12. [12] Kubarski, J.Exponential mapping for Lie groupoids. Applications, Colloquium Mathematicum, Vol. LIV, 1987, 39-48. Zbl0638.22001MR928656
  13. [13] Kubarski, J.Pradines-type groupoids over foliations ; cohomology, connections and the Chern-Weil homomorphism, Preprint Nr 2, Institute of Mathematics, Technical University of Lodz, August 1986. MR946719
  14. [14] Kubarski, J.Lie algebroid of a principal fibre bundle - three equivalent definitions, Prace Naukowe Politechniki Szczecinskiej, 11 (1988), 123-145. Zbl0758.55012MR1129261
  15. [15] Kubarski, J.Lie algebroid of a principal fibre bundle, Publ. Dep. Math.Universite de Lyon 1, 1/A, 1989. Zbl0758.55012MR1129261
  16. [16] 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, Vol. 4, numeros 2 y 3 ; 1991. Zbl0766.17004MR1145691
  17. [17] Kubarski, J.The Chern-Weil homomorphism of regular Lie algebroids, Publ. Dep. Math.Universite de Lyon 1, in printing. Zbl1014.53048
  18. [18] Kubarski, J.Bott's phenomenon in the theory of nonclosed Lie subgroups, in preparation. 
  19. [19] Kubarski, J.Invariant cohomology of Lie algebroids, in preparation. Zbl0996.22005
  20. [20] Mackenzie, K., Lie groupoids and Lie algebroids in differential Geometry, London Mathematical Society Lecture Note Series 124, Cambridge, 1987. Zbl0683.53029MR896907
  21. [21] Mackenzie, K.Algebraic constructions in the category of Lie algebroids, J.Algebra (to appear). Zbl0696.22007MR1037400
  22. [22] Maxim-Raileanu, L., Cohomology of Lie algebroids, An. Sti. Univ. "Al. I. Cuza" Iasi. Sect. I a Mat.XXII f 2 (1976), 197-199. Zbl0361.18013MR438358
  23. [23] Molino, P., Etude des feuilletages transversalement complets et applications, Ann. Sci. École Norm. Sup., 10(3) (1977), 289-307. Zbl0368.57007MR458446
  24. [24] Molino, P.Riemannian Foliations, Progress in Mathematics Vol. 73, BirkhäuserBostonBasel, 1988. Zbl0633.53001MR932463
  25. [25] Moore, C. C. & Schochet, C., Global Analysis on Foliated Spaces, Mathematical Sciences Research Institute publications ; 9. 1988, Springer-VerlagNew-York Inc. Zbl0648.58034MR918974
  26. [26] Ngo-Van-Que, Du prolongement des espaces fibres et des structures infinitesimales, Ann. Inst. Fourier, (Grenoble), 17,1, (1967), 157-223. Zbl0157.28506MR221416
  27. [27] Pelczar, A. & Szarski, J., Wstęp do teorli równań róźniczkowych, Część I (BM66), PWN 1987. MR921032
  28. [28] Pradines, J., Theorie de Lie pour les groupoides differentiables dans la categorie des groupoides, Calcul differential dans la categorie des groupoides infinitesimaux", C. R. Acad. Sci. Ser.A-B, Paris, 264, (1967), 265-248. Zbl0154.21704MR216409
  29. [29] Pradines, J.Theorie de Lie pour les groupoides differentiables, Atti Conv Intern Geom 7 Diff.Bologna, 1967, Bologna-Amsterdam. Zbl0232.22028
  30. [30] Pradines, J.Troisième théorème de Lie pour les groupoides différentiables, C. R. Acad. Sci. Ser.A-B, Paris, 267 (1968), 21-23. Zbl0172.03502MR231414
  31. [31] Sikorski, R., Wstęp do teorli równań róźniczkowej (BM42), PWN 1972. Zbl0255.53001
  32. [32] 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). Zbl0669.58039MR980966

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.