Related papers: Symplectic geography in dimension 8

A non-formal simply connected compact symplectic manifold of dimension 8 is constructed.

In this note, the geography problem in dimension four is reviewed and then its extension to dimension six for the symplectic case is explained. Finally some examples in dimension six are provided.

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.

In this paper, we classify eight-dimensional non-solvable Lie algebras that support a symplectic structure. As well as a complete classification is given, up to symplectomorphism, of eight-dimensional symplectic non-solvable Lie algebras.

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 prove that all complex analytic subvarieties of a generic compact hyperkaehler manifold are even-dimensional. Moreover, these subvarieties are holomorphically symplectic.

Extension of symplectic geometry on manifolds to the supersymmetric case is considered. In the even case it leads to the even symplectic geometry (or, equivalently, to the geometry on supermanifolds endowed with a non-degenerate Poisson…

In this article we consider a version of the geography question for simply-connected symplectic 4-manifolds that takes into account the divisibility of the canonical class as an additional parameter. We also find new examples of 4-manifolds…

We provide a closed, simply connected, symplectic $6$-manifold having infinitely many codimension $2$ symplectic submanifolds. These are mutually homologous but homotopy inequivalent, and furthermore, they cannot admit complex structures.…

We construct a simply connected compact manifold which has complex and symplectic structures but does not admit K\"ahler metrics, in the lowest possible dimension where this can happen, that is, dimension 6. Such a manifold is automatically…

A non completely reducible symplectic Lie algebra is a symplectic Lie algebra which cannot be symplectically reduced to the trivial symplectic Lie algebra. Our aim is to provide a complete classification, up to symplectomorphism of non…

The geography of minimal symplectic 4-manifolds with arbitrary fundamental group and symplectic 6-manifolds with abelian fundamental group of small rank, and with arbitrary fundamental group are addressed.

In this paper we define a new category of almost complex riemannian 4- manifolds and discuss some basic properties of such pseudo symplectic manifolds. Some motivation based on the Seiberg - Witten theory is imposed.

We study the existence of some irreducible projective plane curves of degree~$8$ with some prescribed topological type of singularities in the algebraic and symplectic worlds.

We provide examples of contact manifolds of any odd dimension $\geq 5$ which are not diffeomorphic but have exact symplectomorphic symplectizations.

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…

While symplectic manifolds have no local invariants, they do admit many global numerical invariants. Prominent among them are the so-called symplectic capacities. Different capacities are defined in different ways, and so relations between…

We classify symplectic 4-dimensional semifields over $\mathbb{F}_q$, for $q\leq 9$, thereby extending (and confirming) the previously obtained classifications for $q\leq 7$. The classification is obtained by classifying all symplectic…

We show that complex symplectic structures need not be preserved under small deformations, and we find sufficient conditions for this to happen. We study various cohomologies of compact complex symplectic manifolds, obtaining some…

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.…