相关论文: Compatible Relative Lefschetz Fibrations On Admiss…

A bifibration structure on a $6$-manifold is a map to either the complex projective plane $\mathbb{P}^2$ or a $\mathbb{P}^1$-bundle over $\mathbb{P}^1$, such that its composition with the projection to $\mathbb{P}^1$ is a ($6$-dimensional)…

In analogy with the vector bundle theory we define universal and strongly universal Lefschetz fibrations over bounded surfaces. After giving a characterization of these fibrations we construct very special strongly universal Lefschetz…

We consider simply-connected $4$-manifolds admitting Lefschetz fibrations over the $2$-sphere. We explicitly construct nonhyperelliptic and hyperelliptic Lefschetz fibrations of genus $4$ on simply-connected $4$-manifolds which are exotic…

We construct using Lefschetz fibrations a large family of contact manifolds with the following properties: Any bounding contact embedding into an exact symplectic manifold satisfying a mild topological assumption is non-displaceable and…

The topology of broken Lefschetz fibrations is studied by means of handle decompositions. We consider a slight generalization of round handles, and describe the handle diagrams for all that appear in dimension four. We establish simplified…

We show that there exists a non-trivial simplified broken Lefschetz fibration which has infinitely many homotopy classes of sections. We also construct a non-trivial simplified broken Lefschetz fibration which has a section with…

We prove that any symplectic 4-manifold which is not a rational or ruled surface, after sufficiently many blow-ups, admits an arbitrary number of nonisomorphic Lefschetz fibrations of the same genus which cannot be obtained from one another…

The Arakelov--Parshin rigidity theorem implies that a holomorphic Lefschetz fibration $\pi: M \to S^2$ of genus $g \geq 2$ admits only finitely many holomorphic sections $\sigma:S^2 \to M$. We show that an analogous finiteness theorem does…

We establish the Giroux correspondence in arbitrary dimensions. As corollaries we (i) give an alternate proof of a result of Giroux-Pardon that states that any Weinstein domain is Weinstein homotopic to one which admits a Weinstein…

Using theorems of Eliashberg and McDuff, Etnyre [Et] proved that the intersection form of a symplectic filling of a contact 3-manifold supported by planar open book is negative definite. In this paper, we prove a signature formula for…

We show that for each k > 3 there are infinitely many finite type Stein manifolds diffeomorphic to Euclidean space R^{2k} which are pairwise distinct as symplectic manifolds.

Castro and Ozbagci constructed a trisection of a closed 4-manifold admitting a Lefschetz fibration with a $(-1)$-section such that the corresponding trisection diagram can be explicitly constructed from a monodromy of the Lefschetz…

It was shown by Usher that any fiber sum of Lefschetz fibrations over $S^2$ is minimal, which was conjectured by Stipsicz. We prove that the converse does not hold by showing that there exists an indecomposable minimal genus-2 Lefschetz…

We prove that for any rational number $r\in (2,8)$, there exists a genus-$g$ Lefschetz fibration over the two-sphere with large enough genus-$g$ having the slope is $r$.

We prove that a Lefschetz fibration over the disc that, after compactification, has the same singular fibers as an extremal rational elliptic surface can be obtained by deleting a singular fiber and a section from the rational extremal…

We give an algorithm which produces infinitely many pairwise exotic Stein fillings of the same contact 3-manifolds, applying positive allowable Lefschetz fibrations over the disk. As a corollary, for a large class of Stein fillings, we…

We show that there are vast families of contact 3-manifolds each member of which admits infinitely many Stein fillings with arbitrarily big euler characteristics and arbitrarily small signatures ---which disproves a conjecture of Stipsicz…

A real 3- or 4-manifold has by definition an orientation preserving smooth involution acting on it. We consider Lefschetz fibrations of 4-dimensional manifolds-with-boundary and open book decompositions on their boundary in the existence of…

We discuss $4$-dimensional achiral Lefschetz fibrations bounding $3$-dimensional open books and study their Lefschetz fibration (LF) embedding in a bounded $6$-dimensional manifold, in the sense of Ghanwat--Pancholi. As an application we…

In our previous work, we introduced a simple and explicit method for constructing a positive allowable Lefschetz fibration (PALF) from a $2$-handlebody decomposition of any given compact Stein surface. In this paper, we apply this…