Related papers: Symplectic configurations: a homological and compu…

A log symplectic manifold is a Poisson manifold which is generically nondegenerate. We develop two methods for constructing the symplectic groupoids of log symplectic manifolds. The first is a blow-up construction, corresponding to the…

Motivated by an attempt to better understand the notion of a symplectic stack, we introduce the notion of a symplectic hopfoid, which should be thought of as the analog of a groupoid in the so-called symplectic category. After reviewing…

A venerable problem in combinatorics and geometry asks whether a given incidence relation may be realized by a configuration of points and lines. The classic version of this would ask for algebraic lines over some field or possibly real…

We develop techniques for defining and working with virtual fundamental cycles on moduli spaces of pseudo-holomorphic curves which are not necessarily cut out transversally. Such techniques have the potential for applications as foundations…

We solve the stabilized symplectic embedding problem for four-dimensional ellipsoids into the four-dimensional round ball. The answer is neatly encoded by a piecewise smooth function which exhibits a phase transition from an infinite…

We introduce a streamlined procedure for constructing small symplectic $4$-manifolds via contact gluing, based on a technique invented by David Gay around 2000. We give several applications of this procedure, which produced results…

This paper explains an application of Gromov's h-principle to prove the existence, on any orientable 4-manifold, of a folded symplectic form. That is a closed 2-form which is symplectic except on a separating hypersurface where the form…

This is the first of a series of papers devoted to the topology of symplectic Calabi-Yau $4$-manifolds endowed with certain symplectic finite group actions. We completely determine the fixed-point set structure of a finite cyclic action on…

Friedman and Morgan made the "speculation" that deformation equivalence and diffeomorphism should coincide for algebraic surfaces. Counterexamples, for the hitherto open case of surfaces of general type, have been given in the last years by…

In symplectic topology one uses elliptic methods to prove rigidity results about symplectic manifolds and solutions of Hamiltonian equations on them, where the most basic example is given by geodesics on Riemannian manifolds. Harmonic maps…

The real symplectic Stiefel manifold is the manifold of symplectic bases of symplectic subspaces of a fixed dimension. It features in a large variety of applications in physics and engineering. In this work, we study this manifold with the…

In this paper we prove the connectedness of symplectic ball packings in the complement of a spherical Lagrangian, S^2 or RP^2, in symplectic manifolds that are rational or ruled. Via a symplectic cutting construction this is a natural…

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 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…

Let (M,\omega) be a symplectic manifold, and Sigma a compact Riemann surface. We define a 2-form on the space of immersed symplectic surfaces in M, and show that the form is closed and non-degenerate, up to reparametrizations. Then we give…

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…

This work develops a symplectic framework for quantum computing to be applied to classical Hamiltonian systems, exploiting the intrinsic geometric compatibility between unitary quantum evolution and symplectic phase-space dynamics in a…

We use algebraic arc complexes to prove a homological stability result for symplectic groups with slope 2/3 for rings with finite unitary stable rank. Symplectic groups are here interpreted as the automorphism groups of formed spaces with…

For $(\mathbb{C} P^2 \# 5{\overline {\mathbb{C} P^2}},\omega)$, let $N_{\omega}$ be the number of $(-2)$-symplectic spherical homology classes.We completely determine the Torelli symplectic mapping class group (Torelli SMCG): the Torelli…

The purpose of this paper is to investigate the definition of symplectic structure on a smooth stratified pseudomanifold in the framework of local $\C^{\infty}$-ringed space theory. We introduce a sheaf-theoretic definition of symplectic…