相关论文: Symplectic surgeries from singularities

We consider odd Laplace operators arising in odd symplectic geometry. Approach based on semidensities (densities of weight 1/2) is developed. The role of semidensities in the Batalin--Vilkovisky formalism is explained. In particular, we…

In this remark we discuss a relationship between (co)homology classes of a symplectic manifold realized by symplectic and lagrangian objects. We establish some transversality condition for the classes, realized by symplectic divisors and…

We construct symplectic submanifolds of symplectic manifolds with contact border. The boundary of such submanifolds is shown to be a contact submanifold of the contact border. We also give a topological characterization of the constructed…

A classical way to construct a Lagrangian in a symplectic manifold $\Sigma$ is to let $\Sigma$ appear as a smooth fiber in a Lefschetz fibration. If this is possible the singularities of the fibration induce Lagrangian spheres in $\Sigma$…

Twists of contact structures in dimension 3 and higher are studied in this paper from a viewpoint of contact round surgery. Three kinds of new modifications of contact structures which are higher-dimensional generalizations of the…

The geography problem is usually stated for simply connected symplectic 4-manifolds. When the first cohomology is nontrivial, however, one can restate the problem taking into account how close the symplectic manifold is to satisfying the…

We develop techniques to construct explicit symplectic Lefschetz fibrations over the 2-sphere with any prescribed signature and any spin type when the signature is divisible by 16. This solves a long-standing conjecture on the existence of…

After reviewing recent results on symplectic Lefschetz pencils and symplectic branched covers of CP^2, we describe a new construction of maps from symplectic manifolds of any dimension to CP^2 and the associated monodromy invariants. We…

We compute symplectic cohomology for Milnor fibres of certain compound Du Val singularities that admit small resolution by using homological mirror symmetry. Our computations suggest a new conjecture that the existence of a small resolution…

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…

We study the Euler-Lagrange cohomology and explore the symplectic or multisymplectic geometry and their preserving properties in classical mechanism and classical field theory in Lagrangian and Hamiltonian formalism in each case…

Cosymplectic and normal almost contact structures are analogues of symplectic and complex structures that can be defined on 3-manifolds. Their existence imposes strong topological constraints. Generalized geometry offers a natural common…

The notions of holomorphic symplectic structures and hypercomplex structures on Courant algebroids are introduced and then proved to be equivalent. These generalize hypercomplex triples and holomorphic symplectic 2-forms on manifolds…

Log-symplectic structures are Poisson structures that are determined by a symplectic form with logarithmic singularities. We construct moduli spaces of curves with values in a log-symplectic manifold. Among the applications, we classify…

We follow the study by Cascini-Panov on symplectic generic complex structures on Kahler surfaces with $p_g=0$, a question proposed by Tian-Jun Li, by demonstrating that the one-point blowup of an Enriques surface admits non-Kahler…

This paper develops a symplectic bifurcation theory for integrable systems in dimension four. We prove that if an integrable system has no hyperbolic singularities and its bifurcation diagram has no vertical tangencies, then the fibers of…

We consider structures analogous to symplectic Lefschetz pencils in the context of a closed 4-manifold equipped with a `near-symplectic' structure (ie, a closed 2-form which is symplectic outside a union of circles where it vanishes…

We show that any 4-manifold, after surgery on a curve, admits an achiral Lefschetz fibration. In particular, we show that the connected sum of any simply connected 4-manifold with a 2-sphere bundle over the 2-sphere will admit an achiral…

Using odd symplectic structure constructed over tangent bundle of the symplectic manifold, we construct the simple supergeneralization of an arbitrary Hamiltonian mechanics on it. In the case, if the initial mechanics defines Killing vector…

We study neighborhoods of configurations of symplectic surfaces in symplectic 4-manifolds. We show that suitably `positive' configurations have neighborhoods with concave boundaries and we explicitly describe open book decompositions of the…