Related papers: Symplectic cohomologies and deformations

A hypercomplex structure $(I,J,K)$ on a manifold $M$ is said to be $C^\infty$-pure-and-full if the Dolbeault cohomology $H^{2,0}_{\partial}(M,I)$ is the direct sum of two natural subgroups called the $\bar{J}$-invariant and the…

We prove that all complex analytic subvarieties of a generic compact hyperkaehler manifold are even-dimensional. Moreover, these subvarieties are holomorphically symplectic.

We define Floer homology for a time-independent, or autonomous Hamiltonian on a symplectic manifold with contact type boundary, under the assumption that its 1-periodic orbits are transversally nondegenerate. Our construction is based on…

I prove the existence of slices for an action of a reductive complex Lie group on a K\"ahler manifold at certain orbits, namely those orbits that intersect the zero level set of a momentum map for the action of a compact real form of the…

We prove that any coadjoint orbit with real eigenvalues of a complex semisimple Lie group, equipped with the real part of the canonical holomorphic symplectic form, is symplectomorphic to the cotangent bundle of a (partial) flag manifold.…

Symplectic Field Theory studies J-holomorphic curves in almost complex manifolds with cylindrical ends. One natural generalization is to replace 'cylindrical' by 'asymptotically cylindrical'. In this article, we generalize the asymptotic…

This note discusses the structure of J-holomorphic curves in symplectic 4-manifolds (M,\om) when J\in \Jj(\Ss), the set of \om-tame J for which a fixed chain \Ss of transversally intersecting embedded spheres of self-intersection \le -2 is…

Let (M,I) be a compact Kaehler manifold admitting a hypercomplex structure. We show that (M, I) admits a natural HKT-metric. This is used to construct a holomorphic symplectic form on (M,I).

We give an equivalent definition of compact locally conformally hyperk\"ahler manifolds in terms of the existence of a nondegenerate complex two-form with natural properties. This is a conformal analogue of Beauville's theorem stating that…

In this paper, we introduce a new kind of Siegel upper half space and consider the symplectic geometry on it explicitly under the action of the group of all holomorphic transformations of it. The results and methods will form a basis for…

This paper consists of two parts. In the first part, we use symplectic homology to distinguish the contact structures on the Brieskorn manifolds $\Sigma(2l,2,2,2)$, which contact homology cannot distinguish. This answers a question from…

We develop a family of deformations of the differential and of the pair-of-pants product on the Hamiltonian Floer complex of a symplectic manifold (M,\omega) which upon passing to homology yields ring isomorphisms with the big quantum…

These notes combine material from short lecture courses given in Paris, France, in July 2001 and in Srni, the Czech Republic, in January 2003. They discuss groups of symplectomorphisms of closed symplectic manifolds (M,\om) from various…

We study Hamiltonian systems near a compact symplectic Morse-Bott minimum. Our first result shows that if the flow is Zoll (that is, it induces a free circle action) along a sequence of energy levels converging to the minimum, then the…

We show that simply connected contact manifolds that are subcritically Stein fillable have a unique symplectically aspherical filling up to diffeomorphism. Various extensions to manifolds with non-trivial fundamental group are discussed.…

We study the dynamics of Hamiltonian diffeomorphisms on convex symplectic manifolds. To this end we first establish the Piunikhin-Salamon-Schwarz isomorphism between the Floer homology and the Morse homology of such a manifold, and then use…

We show that a small neighborhood of a closed symplectic submanifold in a geometrically bounded aspherical symplectic manifold has non-vanishing symplectic homology. As a consequence, we establish the existence of contractible closed…

Let M be a compact Riemannian manifold equipped with a parallel differential form \omega. We prove a version of Kaehler identities in this setting. This is used to show that the de Rham algebra of M is weakly equivalent to its subquotient…

We apply Menke's JSJ decomposition for symplectic fillings to several families of contact 3-manifolds. Among other results, we complete the classification up to orientation-preserving diffeomorphism of strong symplectic fillings of lens…

We consider compact K\"ahlerian manifolds $X$ of even dimension 4 or more, endowed with a log-symplectic structure $\Phi$, a generically nondegenerate closed 2-form with simple poles on a divisor $D$ with local normal crossings. A simple…