Related papers: On extensions of a symplectic class

We establish a criterion that ensures a bounded almost complex curve in a bounded almost complex 4-manifold minimizes genus amongst all smooth surfaces that share its homology class and the transverse link on its boundary. An immediate…

A symplectic fibration is a fibre bundle in the symplectic category. We find the relation between deformation quantization of the base and the fibre, and the total space. We use the weak coupling form of Guillemin, Lerman, Sternberg and…

Let X be a compact Kahler holomorphic-symplectic manifold, which is deformation equivalent to the Hilbert scheme of length n subschemes of a K3 surface. Let L be a nef line-bundle on X, such that the 2n-th power of c_1(L) vanishes and…

We continue our previous work to prove that for any non-minimal ruled surface $(M,\omega)$, the stability under symplectic deformations of $\pi_0, \pi_1$ of $Symp(M,\omega)$ is guided by embedded $J$-holomorphic curves. Further, we prove…

We consider the geometric formulation of the Hamiltonian formalism for field theory in terms of {\em Hamiltonian connections} and {\em multisymplectic forms}. In this framework the covariant Hamilton equations for Mechanics and field theory…

We observe that the notion of a trivial Serre fibration, a Serre fibration, and being contractible, for finite CW complexes, can be defined in terms of the Quillen lifting property with respect to a single map M-->/\ of finite topological…

Previously work of the author with Meier and Starkston showed that every closed symplectic manifold $(X,\omega)$ with a rational symplectic form admits a trisection compatible with the symplectic topology. In this paper, we describe the…

We study holomorphic symplectic manifolds which are fibred by abelian varieties. This structure is a higher dimensional analogue of an elliptic fibration on a K3 surface. We investigate when a holomorphic symplectic manifold is fibred in…

In this article, the authors review what the Floer homology is and what it does in symplectic geometry both in the closed string and in the open string context. In the first case, the authors will explain how the chain level Floer theory…

We extend Donaldson's asymptotically holomorphic techniques to symplectic orbifolds. More precisely, given a symplectic orbifold such that the symplectic form defines an integer cohomology class, we prove that there exist sections of large…

In this note we extend to non trivial Hamiltonian fibrations over symplectically uniruled manifolds a result of Lu's, \cite{Lu}, stating that any trivial symplectic product of two closed symplectic manifolds with one of them being…

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 give a general construction of extremal Kaehler metrics on the total space of certain holomorphic submersions, extending results of Dervan-Sektnan, Fine, and Hong. We consider submersions whose fibres admit a degeneration to Kaehler…

In this note we prove that a positive multiple of each even-dimensional integral homology class of a compact symplectic manifold $(M^{2n}, \omega)$ can be represented as the difference of the fundamental classes of two symplectic…

In this paper we study whether symplectic toric manifolds are symplectically cohomologically rigid. Here we say that symplectic cohomological rigidity holds for some family of symplectic manifolds if the members of that family can be…

We construct an explicit topological model (similar to the topological Springer fibers appearing in work of Khovanov and Russell) for every two-row Springer fiber associated with the even orthogonal group and prove that the respective…

Let V be the even part of the vertex operator super-algebra of r pairs of symplectic fermions. Up to two conjectures, we show that V admits a unique holomorphic extension if r is a multiple of 8, and no holomorphic extension otherwise. This…

We study an analogue of fibrations of topological spaces with the homotopy lifting property in the setting of C*-algebra bundles. We then derive an analogue of the Leray-Serre spectral sequence to compute the K-theory of the fibration in…

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…

A topological condition is given, characterizing which closed manifolds in dimensions < 8 (and conjecturally in general) admit symplectic structures. The condition is the existence of a certain fibration-like structure called a hyperpencil.…