Related papers: On subcritically Stein fillable 5-manifolds

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

In this paper we introduce the notion of a formal complex contact structure on an odd dimensional complex manifold. Our main result is that every formal complex contact structure on a Stein manifold $X$ is homotopic to a holomorphic contact…

We prove that closed connected contact manifolds of dimension $\geq 5$ related by an h-cobordism with a flexible Weinstein structure become contactomorphic after some kind of stabilization. We also provide examples of non-conjugate contact…

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…

Two of the basic questions in contact topology are which manifolds admit tight contact structures, and on those that do, can we classify such structures. We present the first such classification on an infinite family of (mostly) hyperbolic…

The aim of this paper is to give an alternative proof of a theorem about the existence of contact structures on five-manifolds due to Geiges. This theorem asserts that simply-connected five-manifolds admit a contact structure in every…

This short paper gives a constraint on Chern classes of closed strictly pseudoconvex CR manifolds (or equivalently, closed holomorphically fillable contact manifolds) of dimension at least five. We also see that our result is ''optimal''…

We prove that all flexible Weinstein fillings of a given contact manifold with vanishing first Chern class have isomorphic integral cohomology; in certain cases, we prove that all flexible fillings are symplectomorphic. As an application,…

We prove, in a geometric way, that the standard contact structure on the real projective space of dimension $2n-1$ is not Liouville fillable for $n \ge 3$ and odd. We also prove that, for all $n$, semipositive fillings of those contact…

This paper investigates the symplectic and contact topology associated to circular spherical divisors. We classify, up to toric equivalence, all concave circular spherical divisors $ D $ that can be embedded symplectically into a closed…

In this note we construct infinitely many distinct simply connected Stein fillings of a certain infinite family of contact 3--manifolds.

Infinitely many contact 3-manifolds each admitting infinitely many, pairwise non-diffeomorphic Stein fillings are constructed. We use Lefschetz fibrations in our constructions and compute their first homologies to distinguish the fillings.

In this work, we prove that every complex contact structure gives rise to a distinguished type of almost contact metric 3-structure. As an application of our main result, we provide several new examples of manifolds which admit taut contact…

We construct a contact 5-manifold supported by infinitely many distinct open books with the identity monodromy and pairwise exotic Stein pages (i.e. pages are pairwise homeomorphic but non-diffeomorphic Stein fillings of a fixed contact…

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 paper the 5-dimensional contact SO(3)-manifolds are classified up to equivariant contactomorphisms. The construction of such manifolds with singular orbits requires the use of generalized Dehn twists. We show as an application that…

In this note we observe that one can contact embed all contact 3-manifolds into a Stein fillable contact structure on the twisted $S^3$-bundle over $S^2$ and also into a unique overtwisted contact structure on $S^3\times S^2$. These results…

In this article, using combinatorial techniques of mapping class groups, we show that a Stein fillable integral homology $3$-sphere supported by an open book decomposition with page a $4$-holed sphere admits a unique Stein filling up to…

In this note we study contact structures on 5-dimensional manifolds. We give a complete answer under the assumption that the Abundance conjecture holds in dimension 5.

For a compact contact manifold it is shown that the anisotropic Folland-Stein function spaces form an algebra. The notion of anisotropic regularity is extended to define the space of Folland-Stein contact diffeomorphisms, which is shown to…