相关论文: Existence of Lefschetz fibrations on Stein and Wei…

Loi-Piergallini and Akbulut-Ozbagci showed that every compact Stein surface admits a Lefschetz fibration over the 2-disk with bounded fibers. In this note we give a more intrinsic alternative proof of this result.

For more than two decades it has been known that any compact Stein surface (of real dimension four) admits a compatible Lefschetz fibration over a two-disk. More recently, Giroux and Pardon have generalized this result by giving a complex…

The existence of a positive allowable Lefschetz fibration on a compact Stein surface with boundary was established by Loi and Piergallini by using branched covering techniques. Here we give an alternative simple proof of this fact and…

Here we prove that up to diffeomorphism every compact Stein manifold W of dimension 2n+2>4 admits a Lefschetz fibration over the two-disk with Stein regular fibers, such that the monodromy of the fibration is a symplectomorphism induced by…

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 provide a complete set of moves relating any two Lefschetz fibrations over the disk having as their total space the same 4-dimensional 2-handlebody up to 2-equivalence. As a consequence, we also obtain moves relating diffeomorphic…

We prove that every closed oriented smooth 4-manifold X admits a broken Lefschetz fibration (aka singular Lefschetz fibration) over the 2-sphere. Given any closed orientable surface F of square zero in X, we can choose the fibration so that…

We address the question of existence of sections of fibrations in two settings. First, we show that a bundle with base a finite 2-complex admits a section if and only if the inclusion of the fiber is $\pi_1$-injective and the associated…

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…

We introduce an idea of constructing Lefschetz fibrations of Weinstein manifolds from Weinstein handle decompositions on them. We prove theorems that formulate the idea for the cases of cotangent bundles and some plumbings. As a corollary,…

The disc property is formulated for domains in $\mathbb{C}^n$. Holomorphic Lipschitz functions enjoy a gain in the order of Lipschitz regularity along the complex tangential direction on domains with disc property. Disc property is studied…

We prove that any finitely presented group can be realized as the fundamental group of a spin Lefschetz fibration over the 2-sphere. We moreover show that any admissible lattice point in the symplectic geography plane below the Noether line…

We describe a Lefschetz fibration of genus one on the disk cotangent bundle of any closed orientable surface S. As a corollary, we obtain an explicit genus one open book decomposition adapted to the canonical contact structure on the unit…

We characterize regularity of Lagrangian submanifolds in Weinstein Lefschetz fibrations, establishing a conjecture of Giroux and Pardon. Our main result is the Weinstein analogue of a closed symplectic Lefschetz pencil result of Auroux,…

We show a Lefschetz theorem for irreducible overconvergent $F$-isocrystals on smooth varieties defined over a finite field. We derive several consequences from it.

Loi-Piergallini, Akbulut-Ozbagci, and Akbulut-Arikan showed that every compact Stein surface admits a positive allowable Lefschetz fibration over the disk $D^2$ with bounded fibers (PALF in short), and they provided constructions of PALF's…

Let $W$ be a nonorientable $4$-dimensional handlebody without $3$- and $4$-handles. We show that $W$ admits a Lefschetz fibration over the $2$-disk, whose regular fiber is a nonorientable surface with nonempty boundary. This is an analogue…

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

In this paper we prove that a deformed tensor product of two Lefschetz algebras is a Lefschetz algebra. We then use this result in conjunction with some basic Schubert calculus to prove that the coinvariant ring of a finite reflection has…

We define the concept of Lefschetz contact pencil and we show the existence of such structures on any contact manifold. The main idea of the proof is a generalization of the Donaldson arguments used in the symplectic case. We will analyze…