Related papers: Exactly fillable contact structures without Stein …

We show that all symplectically aspherical fillings of the unit cotangent bundle of a given odd-dimensional sphere are diffeomorphic to the corresponding unit co-disc bundle. The concept of fittings previously introduced is not needed.

In this article we provide an infinite family of weakly symplectically fillable contact structures with trivial Ozsvath-Szabo contact invariants over Z/2Z. As a consequence of this fact, we show how Heegaard-Floer theory can distinguish…

We construct the first example of a 5-dimensional simply connected compact manifold that admits a K-contact structure but does not admit a semi-regular Sasakian structure. For this, we need two ingredients: (a) to construct a suitable…

We prove $h$-principle for locally conformal symplectic foliations and contact foliations on open manifolds. We interpret the result on $h$ principle of contact foliations in terms of the regular Jacobi structures.

We prove that $(\mathbb{RP}^{2n-1},\xi_{std})$ is not exactly fillable for any $n\ne 2^k$ and there exist strongly fillable but not exactly fillable contact manifolds for all dimension $\ge 5$.

Given a contact structure on a manifold $V$ together with a supporting open book decomposition, Bourgeois gave an explicit construction of a contact structure on $V \times \mathbb{T}^2$. We prove that all such structures are universally…

In this note we provide explicit constructions of exact Lagrangian embeddings of tori and Klein bottles inside the symplectisation of an overtwisted contact three-manifold. Note that any closed exact Lagrangian in the symplectisation is…

We show that an oriented elliptic 3-manifold admits a universally tight positive contact structure iff the corresponding group of deck transformations on $S^3$ preserves a standard contact structure pointwise. We also relate univerally…

We construct a family of Stein fillable contact homology 3-spheres such that each contact structure of the family is supported by an open book with planar page, and a Stein filling of the contact manifold is of Mazur type.

In this note we make several observations concerning symplectic cobordisms. Among other things we show that every contact 3-manifold has infinitely many concave symplectic fillings and that all overtwisted contact 3-manifolds are…

We introduce the notion of asymptotically finitely generated contact structures, which states essentially that the Symplectic Homology in a certain degree of any filling of such contact manifolds is uniformly generated by only finitely many…

First examples of quasi-exactly solvable models describing spin-orbital interaction are constructed. In contrast with other examples of matrix quasi-exactly solvable models discussed in the literature up to now, our models admit (but still…

In this paper we are interested in characterizing the standard contact sphere in terms of dynamically convex contact manifolds which admit a Liouville filling with vanishing symplectic homology. We first observe that if the filling is…

We prove that a closed manifold which admits a symplectic-Lipschitz structure has non-vanishing even-degree cohomology groups with real coefficients. In particular, spheres $S^{2n}, n \geq 2$ do not admit symplectic-Lipschitz structures.

For contact manifolds in dimension three, the notions of weak and strong symplectic fillability and tightness are all known to be inequivalent. We extend these facts to higher dimensions: in particular, we define a natural generalization of…

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.

We construct a contactomorphism of the standard sphere which does not have any translated points, providing a negative answer to a conjecture posed by Sandon.

We construct an infinite family of non-positive open books with once-punctured torus pages that support Stein-fillable contact structures. Combined with a result of Wendl, this allows us to give a complete answer to a long-standing question…

The aim of this work is the study of symplectic structures on 2-step nilmanifolds. We concentrate in the closeness condition, proving that the existence of a closed 2-form of type II is necessary to get a symplectic structure. In low…

In the breakthrough paper [V. Mu\~noz, A Smale-Barden manifold admitting K-contact but not Sasakian structure, 2024, 10.4171/JEMS/1496], it is constructed the first example of a simply connected compact 5-manifold (aka.\ Smale-Barden…