Related papers: Singular polarizations and symplectic embeddings

Let $(X,\omega)$ be a symplectic rational 4 manifold. We study the space of tamed almost complex structures $\mathcal{J}_{\omega}$ using a fine decomposition via smooth rational curves and a relative version of the infinite-dimensional…

In this article we show that every closed oriented smooth 4-manifold can be decomposed into two codimension zero submanifolds (one with reversed orientation) so that both pieces are exact Kahler manifolds with strictly pseudoconvex…

Given an SO(3)-bundle with connection, the associated two-sphere bundle carries a natural closed 2-form. Asking that this be symplectic gives a curvature inequality first considered by Reznikov. We study this inequality in the case when the…

We describe a collection of constructions which illustrate a panoply of ``exotic'' smooth 4-manifolds.

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.…

In this paper, the symplectic genus for any 2-dimensional class in a 4-manifold admitting a symplectic structure is introduced, and its relation with the minimal genus is studied. It is used to describe which classes in rational and…

In this article, we construct infinitley many simply connected, nonsymplectic and pairwise nondiffeomorphic 4-manifolds starting from E(n) and applying the sequence of knot surgery, ordinary blowups and rational blowdown. We also compute…

We construct a new family {K_n} of simply connected symplectic 4-manifolds with the property c_1^2(K_n)/chi(K_n) -> 9 (as n goes to infinity).

We set up a topological framework for degenerations of symplectic manifolds into singular spaces paying a special attention to the behavior of Lagrangian manifolds and their (holomorphic) membranes. We show that degenerations into singular…

Let G be a finite group acting on a symplectic complex vector space V. Assume that the quotient V/G has a holomorphic symplectic resolution. We prove that G is generated by "symplectic reflectionsd"', i.e. symplectomorphisms with fixed…

We show that there is a complex structure on the symplectic 4-manifold $W_{4, k}$ obtained from the elliptic surface E(4) by rationally blowing down $k$ sections for $2\le k\le 9$. And we interpret it via ${\mathbb Q}$-Gorenstein smoothing.…

We present recursive formulas which compute the recently defined "higher symplectic capacities" for all convex toric domains. In the special case of four-dimensional ellipsoids, we apply homological perturbation theory to the associated…

We prove that any symplectic automorphism of finite order of an irreducible holomorphic symplectic manifold of O'Grady's 10-dimensional deformation type is trivial.

This article gives a classification, up to symplectic equivalence, of singular Lagrangian foliations given by a completely integrable system of a 4-dimensional symplectic manifold, in a full neighbourhood of a singular leaf of focus-focus…

Quite recently, McDuff showed that the existence of a symplectic embedding of one four-dimensional ellipsoid into another can be established by comparing their corresponding sequences of ECH capacities. In this note we show that these…

This paper is devoted to the study of symplectic manifolds and their connection with Hamiltonian dynamical systems. We review some properties and operations on these manifolds and see how they intervene when studying the complete…

We show that the pre-order defined on the category of contact manifolds by arbitrary symplectic cobordisms is considerably less rigid than its counterparts for exact or Stein cobordisms: in particular, we exhibit large new classes of…

In the definition of irreducible holomorphic symplectic manifolds the condition of being simply connected can be replaced by vanishing irregularity. We discuss finite quotients X of complex tori where the space of reflexive 2-forms is…

The symplectization of an overtwisted contact structure in Euclidean 3--space is shown to be an exotic symplectic structure on Euclidean 4--space. The technique can be extended to produce exotic symplectic structures in higher dimensional…

We construct a family of pairs of non-isotopic symplectic surfaces in the standard symplectic $4$-disk such that they are bounded by the same transverse knot in the standard contact $3$-sphere and fundamental groups of their complements are…