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Transactions of the American Mathematical Society
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
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1994-1260205-9
PII: S 0002-9947(1994)1260205-9
Keywords: Lie foliations, homotopy groups, homology theories
Article copyright: © Copyright 1994 American Mathematical Society