Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Homotopy groups in Lie foliations

Author: Enrique Macias-Virgós
Journal: Trans. Amer. Math. Soc. 344 (1994), 701-711
MSC: Primary 57R30; Secondary 55N99, 55Q05, 57T10, 57T20
MathSciNet review: 1260205
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: According to the results of Fédida and Molino [9], the structure of a G-Lie foliation F on a compact manifold M can be described by means of four locally trivial fibre bundles. In this paper we study the relations that those fibrations imply among the (rational) homotopy groups of: the manifold M, the generic leaf L, its closure $ N = \bar L$, the basic manifold W, the Lie group G, and the structural Lie group H. Also, we prove that those relations are a particular case of an algebraic result concerning generalized homology theories.

References [Enhancements On Off] (What's this?)

  • [1] P. Caron and Y. Carrière, Flots transversalement de Lie, C. R. Acad. Sci. Paris 280 (1980), 477-478.
  • [2] S. Eilenberg and N. E. Steenrod, Foundations of algebraic topology, Princeton Univ. Press, 1952. MR 0050886 (14:398b)
  • [3] E. Fédida, Sur les feuilletages de Lie, C. R. Acad. Sci. Paris 277 (1971), 999-1002. MR 0285025 (44:2249)
  • [4] Y. Félix, La dichotomie elliptique-hyperbolique en homotopie rationnelle, Astérisque 176, S.M.F., 1989.
  • [5] E. Gallego and A. Reventós, Lie flows of codimension 3, Trans. Amer. Math. Soc. 326 (1991), 529-541. MR 1005934 (91k:53037)
  • [6] E. Ghys, Groupes d'holonomie des feuilletages de Lie, Indag. Math. 47 (1985), 173-182. MR 799078 (87d:57021)
  • [7] R. Hermann, On the differential geometry of foliations, Ann. of Math. (2) 72 (1960), 445-457. MR 0142130 (25:5523)
  • [8] G. Meigniez, Sous-groupes de génération compacte des groupes de Lie résolubles, Université Paris VII, preprint, 1992.
  • [9] P. Molino, Riemannian foliations, Progress in Math., 73, Birkhäuser, 1988. MR 932463 (89b:53054)
  • [10] R. E. Mosher and M. C. Tangora, Cohomology operations and applications in homotopy theory, Harper & Row, 1968. MR 0226634 (37:2223)
  • [11] J. R. Munkres, Elements of algebraic topology, Addison-Wesley, 1984. MR 755006 (85m:55001)
  • [12] C. T. C. Wall, On the exactness of interlocking sequences, Enseign. Math. 12 (1966), 95-100. MR 0206943 (34:6759)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 57R30, 55N99, 55Q05, 57T10, 57T20

Retrieve articles in all journals with MSC: 57R30, 55N99, 55Q05, 57T10, 57T20

Additional Information

Keywords: Lie foliations, homotopy groups, homology theories
Article copyright: © Copyright 1994 American Mathematical Society

American Mathematical Society