Related papers: Pseudoholomorphic discs and symplectic structures …

We first present the construction of the moduli space of real pseudo-holomorphic curves in a given real symplectic manifold. Then, following the approach of Gromov and Witten, we construct invariants under deformation of real rational…

In this paper we will explore fundamental constraints on the evolution of certain symplectic subvolumes possessed by any Hamiltonian phase space. This research has direct application to optimal control and control of conservative mechanical…

We study the space of pseudo-holomorphic spheres in compact symplectic manifolds with convex boundary. We show that the theory of Gromov-Witten invariants can be extended to the class of semi-positive manifolds with convex boundary. This…

We prove a result which establishes restrictions on the pseudoholomorphic curves which can exist in a stable Hamiltonian manifold in the presence of certain $\mathbb{R}$-invariant foliations of the symplectization by holomorphic…

We provide a local approximation result of non-holomorphic discs with small d-bar by pseudoholomorphic ones. As an application, we provide a certain gluing construction.

In this paper we consider symplectic and Hamiltonian structures of systems generated by actions of sigma-model type and show that these systems are naturally connected with specific symplectic geometry on loop spaces of Riemannian and…

We solve a problem on filling by Levi-flat hypersurfaces for a class of totally real 2-tori in a real 4-manifold with an almost complex structure tamed by an exact symplectic form. As an application we obtain a simple proof of Gromov's…

This thesis studies the symplectic structure of holomorphic coadjoint orbits, and their projections. A holomorphic coadjoint orbit O is an elliptic coadjoint orbit which is endowed with a natural invariant K\"ahlerian structure. These…

For any compact almost complex manifold $(M,J)$, the last two authors defined two subgroups $H_J^+(M)$, $H_J^-(M)$ of the degree 2 real de Rham cohomology group $H^2(M, \mathbb{R})$ in arXiv:0708.2520. These are the sets of cohomology…

This paper investigates the geometry of a symplectic 4-manifold $(M,\om)$ relative to a J-holomorphic normal crossing divisor S. Extending work by Biran (in Invent. Math. 1999), we give conditions under which a homology class $A\in…

We consider some differential geometric classes of local and nonlocal Poisson and symplectic structures on loop spaces of smooth manifolds which give natural Hamiltonian and multihamiltonian representations for some important nonlinear…

This is the first of two papers devoted to showing how the rich algebraic formalism of Eliashberg-Givental-Hofer's symplectic field theory (SFT) can be used to define higher algebraic structures on the symplectic cohomology of open…

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…

Symplectic slice theorems elucidate the local structure of symplectic manifolds carrying Hamiltonian actions of compact Lie groups. We generalize these theorems in two natural settings. The first is based on the idea that complex reductive…

While symplectic manifolds have no local invariants, they do admit many global numerical invariants. Prominent among them are the so-called symplectic capacities. Different capacities are defined in different ways, and so relations between…

We study analysis over infinite dimensional manifolds consisted by sequences of almost K\"ahler manifolds. In particular we develop moduli theory of pseudo holomorphic curves into the spaces with high symmetry. As applications, we study…

Let $G$ be a compact connected semisimple Lie group. We extend the techniques of Weinstein [W] to give a construction in group cohomology of symplectic forms $\omega$ on \lq twisted' moduli spaces of representations of the fundamental group…

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…

Deformations of the heterotic superpotential give rise to a topological holomorphic theory with similarities to both Kodaira-Spencer gravity and holomorphic Chern-Simons theory. Although the action is cubic, it is only quadratic in the…

In this paper we introduce invariants of semi-free Hamiltonian actions of $S\sp 1$ on compact symplectic manifolds (which satisfy some technical conditions related to positivity) using the space of solutions to certain gauge theoretical…