On deformations of transversely homogeneous foliations
Identifieur interne : 001151 ( Main/Exploration ); précédent : 001150; suivant : 001152On deformations of transversely homogeneous foliations
Auteurs : A. El Kacimi Alaoui [France] ; G. Guasp [Espagne] ; M. Nicolau [Espagne]Source :
- Topology [ 0040-9383 ] ; 2001.
English descriptors
- KwdEn :
- Abelian, Alaoui, Algebra, Algebra isomorphism, Analytic space, Cauchy subsequence, Cocompact subgroup, Cohomology, Cohomology classes, Cohomology group, Compact manifold, Complex morphism, Cosets, Deformation, Deformation theory, Dexned, Eld, Elliptic, Elliptic operator, Foliation, Global sections, Hermitian, Hilbert space, Hodge, Hodge decomposition, Hodge decomposition theorem, Hodge theorem, Homogeneous foliation, Homogeneous foliations, Homogeneous space, Homogeneous structures, Integrability, Integrability condition, Integrable, Integrable elements, Isomorphic, Isomorphism, Kacimi, Kacimi alaoui, Linear isomorphism, Local coordinates, Morphism, Neighbourhood, Nite, Nite dimension, Open subset, Orthogonal decomposition, Parametrized, Principal bundle, Real line, Regularity lemma, Riemannian, Riemannian foliations, Smooth section, Smooth space, Straightforward computation, Structure constants, Subalgebra, Subgroup, Topology, Vector bundles, Vector space, Versal, Versal space.
- Teeft :
- Abelian, Alaoui, Algebra, Algebra isomorphism, Analytic space, Cauchy subsequence, Cocompact subgroup, Cohomology, Cohomology classes, Cohomology group, Compact manifold, Complex morphism, Cosets, Deformation, Deformation theory, Dexned, Eld, Elliptic, Elliptic operator, Foliation, Global sections, Hermitian, Hilbert space, Hodge, Hodge decomposition, Hodge decomposition theorem, Hodge theorem, Homogeneous foliation, Homogeneous foliations, Homogeneous space, Homogeneous structures, Integrability, Integrability condition, Integrable, Integrable elements, Isomorphic, Isomorphism, Kacimi, Kacimi alaoui, Linear isomorphism, Local coordinates, Morphism, Neighbourhood, Nite, Nite dimension, Open subset, Orthogonal decomposition, Parametrized, Principal bundle, Real line, Regularity lemma, Riemannian, Riemannian foliations, Smooth section, Smooth space, Straightforward computation, Structure constants, Subalgebra, Subgroup, Topology, Vector bundles, Vector space, Versal, Versal space.
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:
- Espagne, France
- Catalogne, Hauts-de-France, Nord-Pas-de-Calais
- Barcelone, Valenciennes
- Université autonome de Barcelone, Université de Valenciennes
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<front><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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