Related papers: Transversal hard Lefschetz theorem on transversely…

The mean flux theorems are proved for solutions of the Helmholtz equation and its modified version. Also, their converses are considered along with some other properties which generalise those that guarantee harmonicity.

The notion of a holomorphically symplectic manifold can be generalized to the singular one. This paper studies the birational contraction maps between symplectic varieties, and then describes the deformation of a symplectic variety which…

We prove a version of the Lefschetz hyperplane theorem for fppf cohomology with coefficients in any finite commutative group scheme over the ground field. As consequences, we establish new Lefschetz results for the Picard scheme.

We study the transversally harmonic maps between foliated Riemannian manifolds. In particular, we prove that under some curvature conditions, any transversally harmonic map is transversally totally geodesic.

The purpose of the notes is to reiterate and expand the viewpoint, outlined in the paper math.AG/0110142 of T. Coates and the author, which recasts the concept of Frobenius manifold in terms of linear symplectic geometry and exposes the…

We prove a normal form theorem for Poisson structures around Poisson transversals (also called cosymplectic submanifolds), which simultaneously generalizes Weinstein's symplectic neighborhood theorem from symplectic geometry and Weinstein's…

We prove localization and integration formulas for the equivariant basic cohomology of Riemannian foliations. As a corollary we obtain a Duistermaat-Heckman theorem for transversely symplectic foliations.

Generalizing local Gromov-Witten theory, in this paper we define a local version of symplectic field theory. When the symplectic manifold with cylindrical ends is four-dimensional and the underlying simple curve is regular by automatic…

This paper can be considered as an extension to our paper [On symplectically harmonic forms on six-dimensional nilmanifolds, Comment. Math. Helv. 76 (2001), n 1, 89-109]. Also, it contains a brief survey of recent results on symplectically…

This article details a construction of symplectic foliations on 3-dimensional orientable riemannian manifolds from harmonic forms; and how it suggests a topological approach to Poisson's equation and newtonian gravity.

In this paper we give an explicit construction of a symplectic Lefschetz fibration whose total space is a smooth compact four dimensional manifold with a prescribed fundamental group. We also study the numerical properties of the sections…

We prove the Relative Hard Lefschetz theorem and the Relative Hodge-Riemann bilinear relations for combinatorial intersection cohomology sheaves on fans.

We apply techniques from symplectic geometry to extend and give a new proof of the complex convexity theorem of Gindikin-Kroetz.

In [11], I. M. Gelfand, V. Retakh, and M. Shubin defined the symplectic sectional curvature of a torsion-free connection preserving a symplectic form. The present article defines the corresponding notion of constant symplectic sectional…

We prove a version the local Reeb-Thurston stability theorem for symplectic foliations.

The long exact sequence describes how the Floer cohomology of two Lagrangian submanifolds changes if one of them is modified by applying a Dehn twist. We give a proof in the simplest case (no bubbling). The paper contains a certain amount…

We obtain new general results on the structure of the space of translation invariant continuous valuations on convex sets (a version of the hard Lefschetz theorem). Using these and our previous results we obtain explicit characterization of…

Firstly we show a generalization of the (1,1)-Lefschetz theorem for projective toric orbifolds and secondly we prove that on 2k-dimensional quasi-smooth hypersurfaces coming from quasi-smooth intersection surfaces, under the Cayley trick,…

In this paper, we prove a higher Lefschetz formula for foliations in the presence of a closed Haefliger current. We associate with such a current an equivariant cyclic cohomology class of Connes' C*-algebra of the foliation, and compute its…

For a symplectic manifold $(M,\omega)$, not necessarily hard Lefschetz, we prove a version of the Merkulov $d\delta$--lemma. We also study the $d\delta$--lemma and related cohomologies for compact symplectic solvmanifolds.