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Zbl 0625.58025
Llabrés, M.; Reventós, A.
Unimodular Lie foliations. (English)
[J] Ann. Fac. Sci. Toulouse, V. Sér., Math. 9, No.2, 243-255 (1988). ISSN 0240-2955

Let ${\cal F}$ be a codimension n Lie ${\cal G}$-foliation on a compact manifold M. We study the relation between H(${\cal G})$ and the cohomology space H(M/${\cal F})$. We show that in general $H\sp *({\cal G})\ne H\sp *(M/{\cal F})$ and we give sufficient conditions for the inclusion $H\sp *({\cal G})\subseteq H\sp *(M/{\cal F})$ and for the equality $H\sp n({\cal G})=H\sp n(M/{\cal F})$. Finally, if ${\cal F}$ is a Lie flow with $H\sp n(M/{\cal F})\ne 0$ we characterize when ${\cal F}$ is homogeneous in terms of its Euler class.

MSC 2000:: *37C85 Dynamics of group actions other than $\bbfZ$ and $\bbfR$, etc.
37C80 Symmetries, equivariant dynamical systems
57R32 Classifying spaces for foliations

Keywords: Lie foliations; basic cohomology

Cited in: Zbl 0897.57001

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