Related papers: Packing symplectic manifolds by hand

We study topological properties of log-symplectic structures and produce examples of compact manifolds with such structures. Notably we show that several symplectic manifolds do not admit log-symplectic structures and several log-symplectic…

In this paper we present an explicit construction of a relative symplectic packing. This confirms the sharpness of the upper bound for the relative packing of a ball into the pair (CP^2, T^2) of the standard complex projective plane and 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.…

An important class of contact 3--manifolds are those that arise as links of rational surface singularities with reduced fundamental cycle. We explicitly describe symplectic caps (concave fillings) of such contact 3--manifolds. As an…

We show an alternative construction of the first example of a simply-connected compact symplectic non-formal 8-manifold given in arXiv:math/0506449. We also give an alternative proof of its non-formality using higher order Massey products.

This is a collection of results on the topology of toric symplectic manifolds. Using an idea of Borisov, we show that a closed symplectic manifold supports at most a finite number of toric structures. Further, the product of two projective…

A method of constructing a class of bihamiltonian structures is presented. Elements of this class are generalizations of the so-called bihamiltonian structures of general position on odd-dimensional manifolds. The method consists in a…

We construct invariants under deformation of real symplectic 4-manifolds. These invariants are obtained by counting three different kinds of real rational J-holomorphic curves which realize a given homology class and pass through a given…

This is a survey paper on the space of symplectic structures on closed 4-manifolds, for the Proceedings ICCM 2004

A survey of finite group actions on symplectic 4-manifolds is given with a special emphasis on results and questions concerning smooth or symplectic classification of group actions, group actions and exotic smooth structures, and…

We prove that, for any n, there are simply-connected four-manifolds which admit n-tuples of symplectic forms whose first Chern classes have pairwise different divisibilities in integral cohomology. It follows that the moduli space of…

Let $(X, \omega, c_X)$ be a real symplectic 4-manifold with real part $R X$. Let $L \subset R X$ be a smooth curve such that $[L] = 0 \in H_1 (R X ; Z / 2Z)$. We construct invariants under deformation of the quadruple $(X, \omega, c_X, L)$…

In this article we consider a version of the geography question for simply-connected symplectic 4-manifolds that takes into account the divisibility of the canonical class as an additional parameter. We also find new examples of 4-manifolds…

The topology of broken Lefschetz fibrations is studied by means of handle decompositions. We consider a slight generalization of round handles, and describe the handle diagrams for all that appear in dimension four. We establish simplified…

Despite spectacular advances in defining invariants for simply connected smooth and symplectic 4-dimensional manifolds and the discovery of effective surgical techniques, we still have been unable to classify simply connected smooth…

In this article, we present new symplectic 4-manifolds with same integral cohomology as $S^{2}\times S^{2}$. The generalization of this construction is given as well, an infinite family of symplectic 4-manifolds cohomology equivalent to…

We prove that the rational blowdown, a surgery on smooth 4-manifolds introduced by Fintushel and Stern, can be performed in the symplectic category. As a consequence, interesting families of smooth 4-manifolds, including the exotic $K3$…

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 study the question of how many embedded symplectic or Lagrangian tori can represent the same homology class in a simply connected symplectic 4-manifold.

We construct embeddings of simplicial complexes into a (surface of a) simplicial ball whose triangulation has bounded degrees and low volume. This construction can be used either to efficiently "simplify a complicated space" by realizing it…