Related papers: Orbits of real forms, Matsuki duality and CR-cohom…

We define a class of compact homogeneous CR manifolds which are bases of Mostow fibrations having total spaces equal to their canonical complex realizations and Hermitian fibers. This is used to establish isomorphisms between their…

We prove a relation between the $\bar\partial_M$ cohomology of a minimal orbit $M$ of a real form $G_0$ of a complex semisimple Lie group $G$ in a flag manifold $G/Q$ and the Dolbeault cohomology of the Matsuki dual open orbit $X$ of the…

We classify homogeneous CR submanifolds in complex hyperbolic spaces arising as orbits of a subgroup of the solvable part of the Iwasawa decomposition of the isometry group of the ambient space.

Motivated by physics, we propose two conjectures regarding the cohomology ring of the crepant resolutions of orbifolds and cohomological invariants of K-equivalent manifolds.

We investigate the $CR$ geometry of the orbits $M$ of a real form $G_0$ of a complex simple group $G$ in a complex flag manifold $X=G/Q$. We are mainly concerned with finite type, Levi non-degeneracy conditions, canonical $G_0$-equivariant…

The purpose of this work is to propose a mixed Hodge structure over a CR manifold. As you know, for a CR manifold, Kohn-Rossi cohomology is naturally introduced. However, the relation between Kohn-Rossi cohomology and De Rham cohomology is…

We study the Bott-Chern cohomology of complex orbifolds obtained as quotient of a compact complex manifold by a finite group of biholomorphisms.

We give explicit harmonic representatives of Dolbeault cohomology of Oeljeklaus-Toma manifolds and show that they are geometrically Dolbeault formal. We also give explicit harmonic representatives of Bott-Chern cohomology of Oeljeklaus-Toma…

In this paper, homology of a contact CR-submanifold of a real hypersurface, which has naturally almost contact metric structure induced from the complex Euclidean space $\mathbb{C}^{m}$, is examined. More precisely, nonexistence of stable…

We study the envelopes of holomorphy of Matsuki orbits $M_{\ell,m,r}$ arising as intersections of $G_0$- and $K$-orbits in complex Grassmannians. These orbits, equipped with natural CR-structures, form a class of compact homogeneous…

We describe the basic Dolbealut cohomology algebra of the canonical foliation on a class of complex manifolds with a torus symmetry group. This class includes complex moment-angle manifolds, LVM- and LVMB-manifolds and, in most generality,…

We consider aspects of the geometry and topology of nilpotent orbits in finite-dimensional complex simple Lie algebras. In particular, we give the equivariant cohomologies of the regular and minimal nilpotent orbits with respect to the…

We study, in some models of Levi flat CR manifolds, the correspondence between the tangential Cauchy-Riemann complex and the complex defined by the associated real foliation.

We establish new results and introduce new methods in the theory of measurable orbit equivalence, using bounded cohomology of group representations. Our rigidity statements hold for a wide (uncountable) class of groups arising from negative…

Orbits of coadjoint representations of classical compact Lie groups have a lot of applications. They appear in representation theory, geometrical quantization, theory of magnetism, quantum optics etc. As geometric objects the orbits were…

We use cross ratios to describe second real continuous bounded cohomology for locally compact topological groups. We also derive a rigidity result for cocycles with values in the isometry group of a proper hyperbolic geodesic metric space.

Motivated by orbifold string theory, we introduce orbifold cohomology group for any almost complex orbifold and orbifold Dolbeault cohomology for any complex orbifold. Then, we show that our new cohomology group satisfies Poincare duality…

A survey of some results and open questions related to the following algebraic invariants of compact complex manifolds, that can be obtained from differential forms: cohomology groups, Chern classes, rational homotopy groups, and higher…

We introduce some compact orbifolds on which there is a certain finite group action having a simple convex polytope as the orbit space. We compute the orbifold fundamental group and homology groups of these orbifolds. We calculate the…

We deal with compact K\"ahler manifolds $M$ acted on by a compact Lie group $K$ of isometries, whose complexification $K^\C$ has exactly one open and one closed orbit in $M$. If the $K$-action is Hamiltonian, we obtain results on the…