Related papers: A new approach to the symplectic isotopy problem

We prove that the group of compactly supported symplectomorphisms of the standard symplectic ball admits a continuum of linearly independent real-valued homogeneous quasimorphisms. In addition these quasimorphisms are Lipschitz in the Hofer…

In 2002 Polterovich has notably established that on closed aspherical symplectic manifolds, Hamiltonian diffeomorphisms of finite order, which we call Hamiltonian torsion, must in fact be trivial. In this paper we prove the first…

We propose a definition of symplectic 2-groupoid which includes integrations of Courant algebroids that have been recently constructed. We study in detail the simple but illustrative case of constant symplectic 2-groupoids. We show that the…

The notion of a symplectic expansion directly relates the topology of a surface to formal symplectic geometry. We give a method to construct a symplectic expansion by solving a recurrence formula given in terms of the…

The purpose of this article is to characterize symplectic and Hamiltonian circle actions on symplectic manifolds in terms of symplectic embeddings of Riemann surfaces. More precisely, we will show that (1) if $(M,\omega)$ admits a…

We investigate spaces of symplectic embeddings of $n\leq 4$ balls into the complex projective plane. We prove that they are homotopy equivalent to explicitly described algebraic subspaces of the configuration spaces of $n$ points. We…

Let $K$ be a compact Lie group. We introduce the process of symplectic implosion, which associates to every Hamiltonian $K$-manifold a stratified space called the imploded cross-section. It bears a resemblance to symplectic reduction, but…

We show that the isomorphism between the moduli space of certain parabolic Higgs bundles over an elliptic curve and the Hilbert scheme of n points of the cotangent bundle of the elliptic curve is a symplectomorphism with respect to their…

We study moduli spaces of meromorphic connections (with arbitrary order poles) over Riemann surfaces together with the corresponding spaces of monodromy data (involving Stokes matrices). Natural symplectic structures are found and described…

We sketch in this article a new theory, which we call Symplectic Field Theory or SFT, which provides an approach to Gromov-Witten invariants of symplectic manifolds and their Lagrangian submanifolds in the spirit of topological field…

In the context of symplectic dynamics, pseudo-rotations are Hamiltonian diffeomorphisms with finite and minimal possible number of periodic orbits. These maps are of interest in both dynamics and symplectic topology. We show that a closed,…

We identify a family of torus representations such that the corresponding singular symplectic quotients at the $0$-level of the moment map are graded regularly symplectomorphic to symplectic quotients associated to representations of the…

We examine symplectic topological features of certain family of monotone Lagrangian submanifolds in CP^n. Firstly, we give a cohomological restriction for Lagrangian submanifolds in CP^n whose first integral homologies are 3-torsion. In…

We present a new and simpler proof of the fact that any Lagrangian $\mathbb{R}P^2$ in $T^*\mathbb{R}P^2$ is Hamiltonian isotopic to the zero section. Our proof mirrors the one given by Li and Wu for the Hamiltonian uniqueness of Lagrangians…

This is the pdf -version of the author's Ph.D. thesis (1995, ULB, Belgium). The notion of symeplectic symmertic space is introduced and studied via Lie theoretical and symplectic geoemetrical methods. The first chapter concerns basic…

In this paper, we demonstrate a relation among Seiberg-Witten invariants which arises from embedded surfaces in four-manifolds whose self-intersection number is negative. These relations, together with Taubes' basic theorems on the…

A famous result of Jurgen Moser states that a symplectic form on a compact manifold cannot be deformed within its cohomology class to an inequivalent symplectic form. It is well known that this does not hold in general for noncompact…

This paper studies the action of symplectic homeomorphisms on smooth submanifolds, with a main focus on the behaviour of symplectic homeomorphisms with respect to numerical invariants like capacities. Our main result is that a symplectic…

Computational topology is a vibrant contemporary subfield and this article integrates knot theory and mathematical visualization. Previous work on computer graphics developed a sequence of smooth knots that were shown to converge point wise…

We prove the bounded isometry conjecture of F. Lalonde and L. Polterovich for a special class of closed symplectic manifolds. As a byproduct, it is shown that the flux group of a product of these special symplectic manifold is isomorphic to…