Related papers: A note on a nontrivial connected component of the …
Let X be a four-manifold with boundary three manifold M. We shall describe (i) a pre-symplectic structure on the space of connections of the trivial SU(n)-bundle over X that comes from the canonical symplectic structure on the cotangent…
We show, in this note, that on any symplectic supermanifold, even or odd, there exist an infinite dimensional affine space of symmetric connections, compatible to the symplectic form.
We provide an infinite family of diffeomorphic symplectic forms on ruled surfaces, which are pairwise non-isotopic. This answers a uniqueness question regarding symplectic structures up to isotopy on closed symplectic four-manifolds.
In this article, we construct the first example of a simply connected minimal symplectic 4-manifold homeomorphic but not diffeomorphic to 3CP^2#7CP^2b. We also construct the first exotic symplectic structure on CP^2#5CP^2b.
This is a survey paper on the space of symplectic structures on closed 4-manifolds, for the Proceedings ICCM 2004
The aim of this note is to present a construction of symplectic structures on orientable globally hyperbolic 4-dimensional lorentzian manifolds. Said structures are defined on the manifold itself, not on its cotangent bundle. It also…
In this paper we shall prove that the singular locus of a symplectic singularity has no codimension 3 irreducible components. As a corollary, a symplectic singularity is terminal if and only if its singular locus has codimension $\geq 4$.…
We construct examples of simply connected nonalgebraic symplectic fourfolds with a prescribed number of nonintersecting symplectic curves with positive self-intersections.
Examples of nonformal simply connected symplectic manifolds are constructed.
This note provides a counterexample to a proposition stated in [J. Differ. Equ. 261.4 (2016) 2528--2551] regarding the neighborhood of certain $4\times 4$ symplectic matrices.
We examine how symplectic cohomology may be used as an invariant on symplectic structures, and investigate the non-uniqueness of these structures on Liouville domains, a field which has seen much development in the past decade. Notably, we…
We analyze the symplectic and complex structures on the panelled web 4-manifolds. In particular, we give infinite family of examples of almost complex but not symplectic and not complex 4-manifolds in the non-simply connected case.
We give examples of generalized complex four-manifolds whose moduli space has infinitely many components.
A non-formal simply connected compact symplectic manifold of dimension 8 is constructed.
We discuss the asymptotic structure of null infinity in five dimensional space-time. Since it is known that the conformal infinity is not useful for odd higher dimensions, we shall employ the coordinate based method like the Bondi…
We give an elementary construction of symplectic connections through reduction. This provides an elegant description of a class of symmetric spaces and gives examples of symplectic connections with Ricci type curvature, which are not…
We consider the moduli space of flat G-bundles over the twodimensional torus, where G is a real, compact, simple Lie group which is not simply connected. We show that the connected components that describe topologically non-trivial bundles…
We present the structure of symplectic cobordism ring $MSp_{*}$ in dimensions up to 51 and give a construction of an infinite series of elements $\Gamma_i$, $ i=1, 3,4, ...$, of order four in this ring, where $\operatorname{dim} \,…
We study the symplectic semi-characteristic of a closed 4n-dimensional symplectic manifold. First, using the even-degree part of the primitive cohomology, we define the symplectic semi-characteristic. Second, using a vector field with…
We study symplectic structures on four-dimensional small covers. Our main result shows that every symplectic four-dimensional small cover is aspherical. We then classify symplectic small covers over products of two polygons, proving that…