Strongly fillable contact 3-manifolds without Stein fillings

We consider a fixed contact 3-manifold that admits infinitely many compact Stein fillings which are all homeomorphic but pairwise non-diffeomorphic. Each of these fillings gives rise to a closed contact 5-manifold described as a contact open book whose page is the filling at hand and whose monodromy is the identity symplectomorphism. We show that the resulting infinitely many contact 5-manifolds are all diffeomorphic but pairwise non-contactomorphic. Moreover, we explicitly d...

Using contact surgery we define families of contact structures on certain Seifert fibered three-manifolds. We prove that all these contact structures are tight using contact Ozsath-Szabo invariants. We use these examples to show that, given a natural number n, there exists a Seifert fibered three-manifold carrying at least n pairwise non-isomorphic tight, not fillable contact structures.

We exhibit a 3-manifold which admits no tight contact structure.

In the first part of this paper, we construct infinitely many hyperbolic closed 3-manifolds which admit no symplectic fillable contact structure. All these 3-manifolds are obtained by Dehn surgeries along L-space knots or L-space two-component links. In the second part of this paper, we show that Dehn surgeries along certain knots and links, including those considered in the first part, admit Stein fillable contact structures as long as the surgery coefficients are sufficient...

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 paper, we find infinite hyperbolic 3-manifolds that admit no weakly symplectically fillable contact structures, using tools in Heegaard Floer theory. We also remark that part of these manifolds do admit tight contact structures.

We continue our study of contact structures on manifolds of dimension at least five using complex surgery theory. We show that in each dimension 2q+1 > 3 there are 'maximal' almost contact manifolds to which there is a Stein cobordism from any other (2q+1)-dimensional contact manifold. We show that the product M x S^2 admits a weakly fillable contact structure provided M admits a weak symplectic filling. We also study the connection between Stein fillability and connected sum...

We determine the closed, oriented Seifert fibered 3-manifolds which carry positive tight contact structures. Our main tool is a new non-vanishing criterion for the contact Ozsvath-Szabo invariant.

In this paper we give explicit, handle-by-handle constructions of concave symplectic fillings of all closed, oriented contact 3-manifolds. These constructions combine recent results of Giroux relating contact structures and open book decompositions of 3-manifolds, earlier results of the author on attaching 4-dimensional symplectic 2-handles along transverse links, and some tricks with mapping class groups of compact surfaces with non-empty boundary.

We use spinal open books to construct contact manifolds with infinitely many different Weinstein fillings in any odd dimension $> 1$, which were previously unknown for dimensions equal to $4n+1$. The argument does not involve understanding factorizations in the symplectic mapping class group.