Related papers: Equivariant basic cohomology under deformations

We give applications of the higher Lefschetz theorems for foliations of [BH10], primarily involving Haefliger cohomology. These results show that the transverse structures of foliations carry important topological and geometric information.…

We prove a generalisation of Bott's vanishing theorem for the full transverse frame holonomy groupoid of any transversely orientable foliated manifold. As a consequence we obtain a characteristic map encoding both primary and secondary…

We investigate the structure of transversely K\"ahler foliations with quasi-negative tranverse Ricci curvature. In particular, we prove a de Rham type theorem decomposition on the leaf space where we characterize each factor.

In this article, the cyclic homology theory of formal deformation quantizations of the convolution algebra associated to a proper etale Lie groupoid is studied. We compute the Hochschild cohomology of the convolution algebra and express it…

We say that a Lie (super)algebra is ''symmetric'' if with every root (with respect to the maximal torus) it has the opposite root of the same multiplicity. Over algebraically closed fields of positive characteristics (up to 7 or 11, enough…

We study the left-orderability of the fundamental groups of cyclic branched covers of links which admit co-oriented taut foliations. In particular we do this for cyclic branched covers of fibred knots in integer homology $3$-spheres and…

For a Riemannian foliation $F$ on a compact manifold $M$ with a bundle-like metric, the de Rham complex of $M$ is $C^{\infty}$-splitted as the direct sum of the basic complex and its orthogonal complement. Then the basic component…

In this paper, we prove that there exists a residual subset of contact forms $\lambda$ (if any) on a compact connected orientable manifold $M$ for which the foliation de Rham cohomology of the associated Reeb foliation $F_\lambda$ is…

In this paper we investigate new applications of the blow-up desingularization method in the context of singular Riemannian foliations. First, we relate the dynamics of such a foliation, which is governed by the so-called Molino sheaf, with…

The basic Dolbeault cohomology groups of a Sasakian manifold M are invariants of its characteristic foliation F (the orbit foliation of the Reeb flow). We show some fundamental properties of this cohomology, which are useful for its…

Consider the Hamiltonian action of a compact connected Lie group on a transversely symplectic foliation which satisfies the transverse hard Lefschetz property. We establish an equivariant formality theorem and an equivariant symplectic…

We construct a deformed algebraic quantum field theory on bifurcate Killing horizons in stationary axisymmetric spacetimes. The deformation is generated by the commuting actions of affine dilations along the null generators of the horizon…

We show that $\phi$-invariant submanifolds of metric contact pairs with orthogonal characteristic foliations make constant angles with the Reeb vector fields. Our main result is that for the normal case such submanifolds of dimension at…

In this article, we study the L2-transverse conformal Killing forms on complete foliated Riemannian manifolds and prove some vanishing theorems. Also, we study the same problems on Kahler foliations with a complete bundle-like metric.

Let f : Y -> X be a morphism of complex projective manifolds, and let F be a subsheaf of the tangent bundle which is closed under the Lie bracket, but not necessarily a foliation. This short paper contains an elementary and very geometric…

Let $\beta$ be a contact form on a compact smooth manifold $X$ and $v_\beta$ its Reeb vector field. The paper applies general results of different authors about Hodge structures that are transversal to a given foliation to the special case…

In this article, we develop a systematic cohomological framework for the study of the rigidity of nilpotent Lie foliations with respect to solvable deformations. We introduce the deformation complex associated to a pair of Lie algebras…

A singular foliation on a complete riemannian manifold M is said to be riemannian if each geodesic that is perpendicular at one point to a leaf remains perpendicular to every leaf it meets. We prove that the regular leaves are equifocal,…

We define the notion of a Killing (super)algebra for a connection on a spinor bundle associated to a generalised spin structure on a pseudo-Riemannian manifold of any signature. We are led naturally to include in the even subspace not only…

In this note we give an explicit formula for the preserved Killing spinors in deformed string theory backgrounds corresponding to integrable Yang--Baxter deformations realized via (sequences of) TsT transformations. The Killing spinors can…