Related papers: A note on positive definite, symplectic four-manif…

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…

Let $M$ be $\CP#2\CPb$, $3\CP#4\CPb$ or $(2n-1)\CP#2n\CPb$ for any integer $n\geq 3$. We construct an irreducible symplectic 4-manifold homeomorphic to $M$ and also an infinite family of pairwise non-diffeomorphic irreducible non-symplectic…

We show that smooth and strongly convex bodies in the symplectic $\mathbb R^{2n}$ for $n>1$ with all characteristics planar, or all outer billiard trajectories planar are affine symplectic images of balls.

We study the formality of the mapping torus of an orientation-preserving diffeomorphism of a manifold. In particular, we give conditions under which a mapping torus has a non-zero Massey product. As an application we prove that there are…

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…

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 prove in this paper that any 4-dimensional symplectic manifold is essentially made of finitely many symplectic ellipsoids. The key tool is a singular analogue of Donaldson's symplectic hypersurfaces in irrational symplectic manifolds.

This short paper shows a topological obstruction of the existence of certain Lagrangian submanifolds in symplectic $4m$-manifolds.

Given an integer b and a finitely presented group G we produce a compact symplectic six-manifold with c_1 = 0, b_2 > b, b_3 > b and fundamental group G. In the simply-connected case we can also arrange for b_3 = 0; in particular these…

We introduce a surgery for generalized complex manifolds whose input is a symplectic 4-manifold containing a symplectic 2-torus with trivial normal bundle and whose output is a 4-manifold endowed with a generalized complex structure…

Two 4-manifolds are stably diffeomorphic if they become diffeomorphic after connected sum with S^2 x S^2's. This paper shows that two closed, orientable, homotopy equivalent, smooth 4-manifolds are stably diffeomorphic, provided a certain…

A study of certain symplectic $4$-orbifolds with vanishing canonical class is initiated. We show that for any such symplectic $4$-orbifold $X$, there is a canonically constructed symplectic $4$-orbifold $Y$, together with a cyclic orbifold…

We show that the homotopy type of a finite oriented Poincar\'{e} 4-complex is determined by its quadratic 2-type provided its fundamental group is finite and has a dihedral Sylow 2-subgroup. By combining with results of Hambleton-Kreck and…

The aim of this paper is to produce infinite exotic structures on smooth closed oriented $4-$manifolds with fundamental group isomorphic to the infinite dihedral group, assuming that $b_2^+$ and $b_2^-$ are at least $12$.

We consider 6-manifolds endowed with a symplectic half-flat SU(3)-structure and acted on by a transitive Lie group G of automorphisms. We review a classical result allowing to show the non-existence of compact non-flat examples. In the…

We prove that a Weinstein domain symplectically embedded in a closed symplectic manifold always admits symplectic hypersurfaces in its complement, possibly after a deformation. As a consequence, we obtain an obstruction for a closed…

The purpose of this paper is to investigate the following problem: For a fixed 2-dimensional homology class K in a simply connected symplectic 4-manifold, up to smooth isotopy, how many connected smoothly embedded symplectic submanifolds…

For a symplectic manifold $(M,\om)$ with exact symplectic form we construct a 2-cocycle on the group of symplectomorphisms and indicate cases when this cocycle is not trivial.

We construct infinitely many smooth 4-manifolds which are homotopy equivalent to $S^2$ but do not admit a spine, i.e., a piecewise-linear embedding of $S^2$ which realizes the homotopy equivalence. This is the remaining case in the…

We construct simply connected, minimal, symplectic 4-manifolds with exotic smooth structures and each with one Seiberg-Witten basic class up to sign, on the Noether line and between the Noether and half Noether lines by star surgeries…