Related papers: On nonformal simply connected symplectic manifolds
Examples of nonformal simply connected symplectic manifolds are constructed.
A non-formal simply connected compact symplectic manifold of dimension 8 is constructed.
We introduce the concept of s-formal minimal model as an extension of formality. We prove that any orientable compact manifold M, of dimension 2n or (2n-1), is formal if and only if M is (n-1)-formal. The formality and the hard Lefschetz…
We construct examples of non-formal simply connected and compact oriented manifolds of any dimension bigger or equal to 7.
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…
We consider the existence of symplectic and conformal symplectic codimension-one foliations on closed manifolds of dimension at least 5. Our main theorem, based on a recent result by Bertelson-Meigniez, states that in dimension at least 7…
We provide examples of contact manifolds of any odd dimension $\geq 5$ which are not diffeomorphic but have exact symplectomorphic symplectizations.
We answer a question of Oprea-Tralle on the realizability of symplectic algebras by symplectic manifolds in dimensions divisible by four, along with a question of Lupton-Oprea in all even dimensions. This will also allow us to address, in…
We show an alternative construction of the first example of a simply-connected compact symplectic non-formal 8-manifold given in arXiv:math/0506449. We also give an alternative proof of its non-formality using higher order Massey products.
In this paper we construct non-simply connected contact manifolds $M$ of dimension $\geq5$ such that $M\times S^1$ does not admit 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…
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…
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…
We prove that the topological complexity of every symplectically atoroidal manifold is equal to twice its dimension. This is the analogue for topological complexity of a result of Rudyak and Oprea, who showed that the…
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 study some symplectic geometric aspects of rationally connected 4-folds. As a corollary, we prove that any smooth projective 4-fold symplectic deformation equivalent to a Fano 4-fold of pseudo-index at least 2 or a rationally connected…
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 study symplectic geometry of rationally connected $3$-folds. The first result shows that rationally connectedness is a symplectic deformation invariant in dimension $3$. If a rationally connected $3$-fold $X$ is Fano or $b_2(X)=2$, we…
The first example of a compact manifold admitting both complex and symplectic structures but not admitting a K\"ahler structure is the renowned Kodaira-Thurston manifold. We review its construction and show that this paradigm is very…
In this article we use the technique of Luttinger surgery to produce small examples of simply connected and non-simply connected minimal symplectic 4-manifolds. In particular, we construct: (1) An example of a minimal symplectic 4-manifold…