Related papers: Lefschetz Fibrations on Compact Stein Manifolds

Given two open books with equal pages we show the existence of an exact symplectic cobordism whose negative end equals the disjoint union of the contact manifolds associated to the given open books, and whose positive end induces the…

We introduce a direct generalization of the Weinstein conjecture to closed, Lichnerowicz exact, locally conformally symplectic manifolds, (for short $\lcs$ manifolds). This conjectures existence of certain 2-curves in the manifold, which we…

We prove that the monodromy diffeomorphism of a complex 2-dimensional isolated hypersurface singularity of weighted-homogeneous type has infinite order in the smooth mapping class group of the Milnor fiber, provided the singularity is not a…

We show that every smooth closed oriented four-manifold admits a decomposition into two co- dimension zero submanifolds with common boundary. Each of these submanifolds carries a structure of a symplectic manifold with pseudo-convex…

A foliation $(M,\mathcal{F})$ is said to be $2$--calibrated if it admits a closed 2-form $\omega$ making each leaf symplectic. By using approximately holomorphic techniques, a sequence $W_k$ of $2$--calibrated submanifolds of…

For any finitely presentable group $G$, we show the existence of an isolated complex surface singularity link which admits infinitely many exotic Stein fillings such that the fundamental group of each filling is isomorphic to $G$. We also…

In the literature, there are two different versions of Hard Lefschetz theorems for a compact Sasakian manifold. The first version, due to Kacimi-Alaoui, asserts that the basic cohomology of a compact Sasakian manifold satisfies the…

In this paper we classify symplectic Lefschetz fibrations (with empty base locus) on a four-manifold which is the product of a three-manifold with a circle. This result provides further evidence in support of the following conjecture…

We study necessary and sufficient conditions for a 4-dimensional Lefschetz fibration over the 2-disk to admit a $\text{Pin}^{\pm}$-structure, extending the work of A. Stipsicz in the orientable setting. As a corollary, we get existence…

The purpose of this paper is to establish several new results about the Hodge theory of Lagrangian fibrations on (not necessarily compact) holomorphic symplectic manifolds. Let $M$ be a holomorphic symplectic manifold of dimension $2n$ that…

We prove that a Weinstein domain symplectically embedded in a closed symplectic manifold always admits symplectic hypersurfaces in its complement, possibly after a deformation. As a consequence, we obtain an obstruction for a closed…

We prove that the existence of regular Lagrangians can be given by existence of Weinstein Lefschetz fibrations with an hypothesis.

For every integer $g \,\geq\, 2$ we show the existence of a compact Riemann surface $\Sigma$ of genus $g$ such that the rank two trivial holomorphic vector bundle ${\mathcal O}^{\oplus 2}_{\Sigma}$ admits holomorphic connections with…

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 determine parts of the contact homology of certain contact 3-manifolds in the framework of open book decompositions, due to Giroux. We study two cases: when the monodromy map of the compatible open book is periodic and when it is…

We study diffeomorphisms of compact, oriented surfaces, developing methods of distinguishing those which have positive factorizations into Dehn twists from those which satisfy the weaker condition of right veering. We use these to construct…

Shapes of four dimensional spaces can be studied effectively via maps to standard surfaces. We explain, and illustrate by quintessential examples, how to simplify such generic maps on 4-manifolds topologically, in order to derive simple…

We give a generalization of the concept of near-symplectic structures to 2n dimensions. According to our definition, a closed 2-form \omega on a 2n-manifold M is near-symplectic, if it is symplectic outside a submanifold Z of codimension 3,…

It is shown that any open Riemann surface can be immersed in any Stein manifold with (volume) density property and of dimension at least 2, if the manifold possesses an exhaustion with holomorphically convex compacts such that their…

We initiate a study of positive multisections of Lefschetz fibrations via positive factorizations in framed mapping class groups of surfaces. Using our methods, one can effectively capture various interesting symplectic surfaces in…