Related papers: Leafwise Coisotropic Intersections
This short note provides a symplectic analogue of Vaisman's theorem in complex geometry. Namely, for any compact symplectic manifold satisfying the hard Lefschetz condition in degree 1, every locally conformally symplectic structure is in…
The harmonic cohomology of a Donaldson symplectic submanifold and of an Auroux symplectic submanifold are compared with that of its ambient space. We also study symplectic manifolds satisfying a weakly Lefschetz property, that is, the…
We define a family of symplectic invariants which obstruct exact symplectic embeddings between Liouville manifolds, using the general formalism of linearized contact homology and its L-infinity structure. As our primary application, we…
We construct examples of simply connected nonalgebraic symplectic fourfolds with a prescribed number of nonintersecting symplectic curves with positive self-intersections.
In previous works, we have introduced the blown-up intersection cohomology and used it to extend Sullivan's minimal models theory to the framework of pseudomanifolds, and to give a positive answer to a conjecture of M. Goresky and W. Pardon…
In this article we define intersection Floer homology for exact Lagrangian cobordisms between Legendrian submanifolds in the contactisation of a Liouville manifold, provided that the Chekanov-Eliashberg algebras of the negative ends of the…
We give an overview of various recent results concerning the topology of symplectic 4-manifolds and singular plane curves, using branched covers and isotopy problems as a unifying theme. While this paper does not contain any new results, we…
Examples of nonformal simply connected symplectic manifolds are constructed.
We investigate the extrinsic topology of Lagrangian submanifolds and of their submanifolds in closed symplectic manifolds using Floer homological methods. The first result asserts that the homology class of a displaceable monotone…
In this paper we study the hemi-slant submanifolds of cosymplectic manifolds. Necessary and sufficient conditions for distributions to be integrable are worked out. Some important results are obtained in this direction.
We investigate quantitative properties of exact locally conformally symplectic (LCS) manifolds, namely the homotheties of the Lee form that still produce an exact LCS form. This gives the notion of elasticity of an exact LCS pair. Using…
We prove a coisotropic embedding theorem \`a l\`a Gotay for pre-multisymplectic manifolds.
This paper is a study of almost contact statistical manifolds. Especially this study is focused on almost cosymplectic statistical manifolds. We obtained basic properties of such manifolds. It is proved a characterization theorem and a…
In this paper we study the coisotropic reduction in different types of dynamics according to the geometry of the corresponding phase space. The relevance of the coisotropic reduction is motivated by the fact that these dynamics can always…
We introduce scattering-symplectic manifolds, manifolds with a type of minimally degenerate Poisson structure that is not too restrictive so as to have a large class of examples, yet restrictive enough for standard Poisson invariants to be…
This is a survey article on symplectically aspherical manifolds. The paper contains a discussion on constructions of symplectically aspherical manifolds, their topological properties and the role of this class in symplectic topology.…
We show that smooth well formed weighted complete intersections have finite automorphism groups, with several obvious exceptions.
We prove a generalized mirror conjecture for non-negative complete intersections in symplectic toric manifolds. Namely, we express solutions of the PDE system describing quantum cohomology of such a manifold in terms of suitable…
Using the structural theorems developed in [Hua13], we study the deformation theory of coisotropic submanifolds in contact manifolds, under the assumption that the characteristic foliation is nonsingular. In the "middle" dimensions, we find…
We prove that symplectic cohomology for open convex symplectic manifolds is invariant when the symplectic form undergoes deformations which may be non-exact and non-compactly supported, provided one uses the correct local system of…