Homotopy groups in Lie foliations

Macias-Virgós, Enrique

doi:10.1090/S0002-9947-1994-1260205-9

Homotopy groups in Lie foliations
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by Enrique Macias-Virgós

Trans. Amer. Math. Soc. 344 (1994), 701-711

DOI: https://doi.org/10.1090/S0002-9947-1994-1260205-9

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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

Flots transversalement de Lie

280

Samuel Eilenberg and Norman Steenrod, Foundations of algebraic topology, Princeton University Press, Princeton, N.J., 1952. MR 0050886
Edmond Fedida, Sur les feuilletages de Lie, C. R. Acad. Sci. Paris Sér. A-B 272 (1971), A999–A1001 (French). MR 285025

La dichotomie elliptique-hyperbolique en homotopie rationnelle

E. Gallego and A. Reventós, Lie flows of codimension $3$, Trans. Amer. Math. Soc. 326 (1991), no. 2, 529–541. MR 1005934, DOI 10.1090/S0002-9947-1991-1005934-4
Étienne Ghys, Groupes d’holonomie des feuilletages de Lie, Nederl. Akad. Wetensch. Indag. Math. 47 (1985), no. 2, 173–182 (French). MR 799078
Robert Hermann, On the differential geometry of foliations, Ann. of Math. (2) 72 (1960), 445–457. MR 142130, DOI 10.2307/1970226

Sous-groupes de génération compacte des groupes de Lie résolubles

Pierre Molino, Riemannian foliations, Progress in Mathematics, vol. 73, Birkhäuser Boston, Inc., Boston, MA, 1988. Translated from the French by Grant Cairns; With appendices by Cairns, Y. Carrière, É. Ghys, E. Salem and V. Sergiescu. MR 932463, DOI 10.1007/978-1-4684-8670-4
Robert E. Mosher and Martin C. Tangora, Cohomology operations and applications in homotopy theory, Harper & Row, Publishers, New York-London, 1968. MR 0226634
James R. Munkres, Elements of algebraic topology, Addison-Wesley Publishing Company, Menlo Park, CA, 1984. MR 755006
C. T. C. Wall, On the exactness of interlocking sequences, Enseign. Math. (2) 12 (1966), 95–100. MR 206943