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On deformations of transversely homogeneous foliations

Identifieur interne : 001151 ( Main/Exploration ); précédent : 001150; suivant : 001152

On deformations of transversely homogeneous foliations

Auteurs : A. El Kacimi Alaoui [France] ; G. Guasp [Espagne] ; M. Nicolau [Espagne]

Source :

RBID : ISTEX:8D6232F1C92D7D0D89E9C34EBBB68D24676D0189

English descriptors

Abstract

Abstract: A transversely homogeneous foliation is a foliation whose transverse model is a homogeneous space G/H. In this paper we consider the class of transversely homogeneous foliations F on a manifold M which can be defined by a family of 1-forms on M fulfilling the Maurer–Cartan equation of the Lie group G. This class includes as particular cases Lie foliations and certain homogeneous spaces foliated by points. We develop, for the foliations belonging to this class, a deformation theory for which both the foliation F and the model homogeneous space G/H are allowed to change. As the main result we show that, under some cohomological assumptions, there exist a versal space of deformations of finite dimension for the foliations of the class and when the manifold M is compact. Some concrete examples are discussed.

Url:
DOI: 10.1016/S0040-9383(00)00017-3


Affiliations:


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<div type="abstract" xml:lang="en">Abstract: A transversely homogeneous foliation is a foliation whose transverse model is a homogeneous space G/H. In this paper we consider the class of transversely homogeneous foliations F on a manifold M which can be defined by a family of 1-forms on M fulfilling the Maurer–Cartan equation of the Lie group G. This class includes as particular cases Lie foliations and certain homogeneous spaces foliated by points. We develop, for the foliations belonging to this class, a deformation theory for which both the foliation F and the model homogeneous space G/H are allowed to change. As the main result we show that, under some cohomological assumptions, there exist a versal space of deformations of finite dimension for the foliations of the class and when the manifold M is compact. Some concrete examples are discussed.</div>
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