Related papers: New symplectic 4--manifolds with $b_+{=}1$
In this paper we study complex symplectic manifolds, i.e., compact complex manifolds $X$ which admit a holomorphic $(2, 0)$-form $\sigma$ which is $d$-closed and non-degenerate, and in particular the Beauville-Bogomolov-Fujiki quadric…
In this note we prove that, for any integer n, there exist a smooth 4-manifold, homotopic to a K3 surface, defined by applying the link surgery method of Fintushel-Stern to a certain 2-component graph link, which admits n inequivalent…
By a special symplectic connection we mean a torsion free connection which is either the Levi-Civita connection of a Bochner-K\"ahler metric of arbitrary signature, a Bochner-bi-Lagrangian connection, a connection of Ricci type or a…
One approach to produce a pair of homeomorphic-but-not-diffeomophic closed 4-manifolds is to find a knot which is smoothly slice in one but not the other. This approach has never been run successfully. We give the first examples of a pair…
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…
In this note we apply a 4-fold sum operation to develop an associativity rule for the pairwise symplectic sum. This allows us to show that certain diffeomorphic symplectic $4$-manifolds made out of elliptic surfaces are in fact…
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.…
It is shown that there are infinitely many compact orientable smooth 4-manifolds which do not admit Einstein metrics, but nevertheless satisfy the strict Hitchin-Thorpe inequality 2 chi > 3 |tau|. The examples in question arise as…
This paper expands some of the issues of the paper math.SG/0506449. We introduce a new technique to produce symplectic manifolds, by taking a symplectic non-free action of a finite group on a symplectic manifold and resolving symplectically…
A Hermitian symplectic manifold is a complex manifold endowed with a symplectic form $\omega$, for which the bilinear form $\omega(I\cdot,\cdot)$ is positive definite. In this work we prove $dd^c$-lemma for 1- and (1,1)-forms for compact…
We study the hard Lefschetz property on compact symplectic solvmanifolds, i.e., compact quotients $M=\Gamma\backslash G$ of a simply-connected solvable Lie group $G$ by a lattice $\Gamma$, admitting a symplectic structure.
We introduce a method to resolve a symplectic orbifold into a smooth symplectic manifold. Then we study how the formality and the Lefschetz property of the symplectic resolution are compared with that of the symplectic orbifold. We also…
Our main result gives an adjunction inequality for embedded surfaces in certain $4$-manifolds with contact boundary under a non-vanishing assumption on the Bauer--Furuta type invariants. Using this, we give infinitely many knots in $S^3$…
The purpose of this paper is to present some results on the existence of homologous, nonisotopic symplectic or lagrangian surfaces embedded in a simply connected symplectic 4-dimensional manifold.
In this article we construct a minimal symplectic 4-manifold R that has small Euler characteristic (e(R)=8) and two essential Lagrangian tori with nice properties. These properties make R particularly suitable for constructing interesting…
We outline the current state of knowledge regarding geometric inequalities of systolic type, and prove new results, including systolic freedom in dimension 4. Namely, every compact, orientable, smooth 4-manifold X admits metrics of…
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…
We investigate the $\mathrm{Pin}^-(2)$-monopole invariants of symplectic $4$-manifolds and K\"{a}hler surfaces with real structures. We prove the nonvanishing theorem for real symplectic $4$-manifolds which is an analogue of Taubes'…
Let (m,b) a pair of natural numbers. For m even (resp. m odd and b greater than or equal to 2) we show that if there is an m-dimensional non-formal compact oriented manifold whose first Betti number equals b, there is also a symplectic…
Let $M$ be a closed oriented $4$-manifold admitting a rank-$2$ oriented foliation with a metric of leafwise positive scalar curvature. If $b^+>1$, then we will show that the Seiberg-Witten invariant vanishes for all \spinc structures.