Related papers: Planar open books with four binding components

Recently, Honda, Kazez and Matic described an adapted partial open book of a compact contact 3-manifold with convex boundary by generalizing the work of Giroux in the closed case. They also implicitly established a one-to-one correspondence…

A strongly non-degenerate mixed function has a Milnor open book structures on a sufficiently small sphere. We introduce the notion of {\em a holomorphic-like} mixed function and we will show that a link defined by such a mixed function has…

We derive new existence results for tight contact structures on certain 3-manifolds which can be presented as surgery along specific knots in S^3. Indeed, we extend our earlier results on knots with maximal Thurston-Bennequin number being…

We investigate nicely embedded H--holomorphic maps into stable Hamiltonian three--manifolds. In particular we prove that such maps locally foliate and satisfy a no--first--intersection property. Using the compactness results of…

The algorithm given by Akbulut-Ozbagci constructs an explicit open book decomposition on a contact three-manifold described by a contact surgery on a link in the three-sphere. In this article, we will improve this algorithm by using…

Thanks to a result of Lisca and Matic and a refinement by Plamenevskaya, it is known that on a 4-manifold with boundary Stein structures with non-isomorphic Spinc structures induce contact structures with distinct Ozsvath-Szabo invariants.…

We show that any compact symplectic manifold (W,\omega) with boundary embeds as a domain into a closed symplectic manifold, provided that there exists a contact plane \xi on dW which is weakly compatible with omega, i.e. the restriction…

We prove that in dimension 3 every nondegenerate contact form is carried by a broken book decomposition. As an application we get that if M is a closed irreducible oriented 3-manifold that is not a graph manifold, for example a hyperbolic…

We give formulae for the Ozsvath-Szabo invariants of 4-manifolds X obtained by fiber sum of two manifolds M_1, M_2 along surfaces S_1, S_2 having trivial normal bundle and genus g>0. The formulae follow from a general theorem on the…

We introduce an essential open book foliation, a refinement of the open book foliation, and develop technical estimates of the fractional Dehn twist coefficient (FDTC) of monodromies and the FDTC for closed braids, which we introduce as…

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…

We introduce a contact invariant in the bordered sutured Heegaard Floer homology of a three-manifold with boundary. The input for the invariant is a contact manifold $(M, \xi, \mathcal{F})$ whose convex boundary is equipped with a signed…

We use the Ozsvath-Szabo contact invariant to produce examples of strongly symplectically fillable contact 3-manifolds which are not Stein fillable.

We show that the canonical contact structure on the link of a normal complex singularity is universally tight. As a corollary we show the existence of closed, oriented, atoroidal 3-manifolds with infinite fundamental groups which carry…

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 take advantage of the correspondence between fibered links, open book decompositions and contact structures on a closed connected 3-dimensional manifold to determine a mixed link diagram presentation for a particular fibered link $L$ in…

We develop the details of a surgery theory for contact manifolds of arbitrary dimension via convex structures, extending the 3-dimensional theory developed by Giroux. The theory is analogous to that of Weinstein manifolds in symplectic…

We demonstrate how to combinatorially calculate the EH-class of a compatible contact structure in the sutured Floer homology group of a balanced sutured three manifold which is associated to an abstract partial open book decomposition. As…

On small Seifert fibered spaces $M(e_0;r_1,r_2,r_3)$ with $e_0\neq-1,-2,$ all tight contact structures are Stein fillable. This is not the case for $e_0=-1$ or $-2$. However, for negative twisting structures it is expected that they are all…

It is known by A. Loi and R. Piergallini that a closed, oriented, smooth 3-manifold is Stein fillable if and only if it has a positive open book decomposition. In the present paper we will show that for every link L in a Stein fillable…