Related papers: Compact Lie algebras, transversely Lie foliations …

The purpose of this paper is to show that any extension of a minimal Lie foliation on a compact manifold is a transversaly Riemannian g\h- foliation with trivial normal bundle. This result permits to classify the extensions of a minimal Lie…

We combine classic stability results for foliations with recent results on deformations of Lie groupoids and Lie algebroids to provide a cohomological characterization for rigidity of compact foliations on compact manifolds.

Motivated by index theory for semisimple groups, we study the relationship between the foliation C^*-algebras on manifolds admitting multiple fibrations. Let F_1,...,F_r be a collection of smooth foliations of a manifold X. We impose a…

In this paper we try to generalize the Haefliger theorem on completly solvable Lie foliations. We prove that: every completely solvable Lie foliation on a compact manifold is the inverse image of a homogenus foliation. Every manifold in…

In previous work by El Kacimi Alaoui-Guasp-Nicolau, a cohomological criterion is given for a Lie $\mathfrak{g}$-foliation on a compact manifold to be rigid among nearby Lie foliations. Our aim is to look for examples of this rigidity…

We study Lie foliations on compact manifolds whose transverse group is \emph{metabelian} (a natural generalization of the affine group $\GA$ considered in earlier work). We establish a complete classification of $\GA$-Lie foliations in…

In this work, we study Lie groupoids equipped with multiplicative foliations and the corresponding infinitesimal data. We determine the infinitesimal counterpart of a multiplicative foliation in terms of its core and sides together with a…

We show that a compact manifold admitting a Killing foliation with positive transverse curvature fibers over finite quotients of spheres or weighted complex projective spaces, provided that the singular foliation defined by the closures of…

We show how locally smooth actions of compact Lie groups on a manifold $X$ can be used to obtain new upper bounds for the topological complexity $\TC(X)$, in the sense of Farber. We also obtain new bounds for the topological complexity of…

In this paper, we prove that a compact K\"ahler manifold $X$ with semi-positive holomorphic sectional curvature admits a locally trivial fibration $\phi \colon X \to Y$, where the fiber $F$ is a rationally connected projective manifold and…

We prove that Riemannian foliations on complete contractible manifolds have a closed leaf, and that all leaves are closed if one closed leaf has a finitely generated fundamental group. Under additional topological or geometric assumptions…

We study smooth foliations of arbitrary codimension on homogeneous compact K\"ahler manifolds. We prove that smooth foliations on rational compact homogeneous manifolds are locally trivial fibrations and classify the smooth foliations with…

We call a foliation $\mathcal{F}$ on a compact manifold infinitesimally rigid if its deformation cohomology $H^{1}(\mathcal{F},N\mathcal{F})$ vanishes. This paper studies infinitesimal rigidity for a distinguished class of Riemannian…

In this article we endow the group of bisections of a Lie groupoid with compact base with a natural locally convex Lie group structure. Moreover, we develop thoroughly the connection to the algebra of sections of the associated Lie…

We extend the Siu--Beauville theorem to a certain class of compact Kaehler--Weyl manifolds, proving that they fiber holomorphically over hyperbolic Riemannian surfaces whenever they satisfy the necessary topological hypotheses. As…

We prove that a transversely holomorphic foliation which is transverse to the fibers of a fibration, is a Seifert fibration if the set of compact leaves is not of zero measure. Similarly, we prove that a finitely generated subgroup of…

We study sheaves of Lie-Rinehart algebras over locally ringed spaces. We introduce morphisms and comorphisms of such sheaves and prove factorization theorems for each kind of morphism. Using this notion of morphism, we obtain (higher)…

We prove a theorem that gives a sufficient condition for the full basic automorphism group of a complete Cartan foliation to admit a unique (finite-dimensional) Lie group structure in the category of Cartan foliations. Emphasize that the…

The purpose of this paper is to develop a Lie algebraic approach to obtain new proofs of important results of H.-C. Wang, Tits and Wolf-Wang-Ziller on compact complex homogeneous manifolds emphasizing only those that admit a transitive…

In this paper we study (smooth and holomorphic) foliations which are invariant under transverse actions of Lie groups.