Related papers: Lefschetz pencils and finitely presented groups

Every finitely presented group is the fundamental group of the total space of a Lefschetz fibration. This follows from results of Gompf and Donaldson, and was also proved by Amoros-Bogomolov-Katzarkov-Pantev. We give another proof by…

It is known that every finitely presented group is the fundamental group of the total space of a Lefschetz fibration. In this paper, we give another proof which improves the result of Korkmaz. In addition, Korkmaz defined the genus of a…

In this paper we give an explicit construction of a symplectic Lefschetz fibration whose total space is a smooth compact four dimensional manifold with a prescribed fundamental group. We also study the numerical properties of the sections…

Generalizing work of I. Baykur, K. Hayano, and N. Monden (arXiv:1903.02906), we construct infinite families of symplectic 4-dimensional manifolds, obtained as total spaces of Lefschetz pencils constructed by explicit monodromy…

Symplectic four-manifolds give rise to Lefschetz fibrations, which are determined by monodromy representations of free groups in mapping class groups. We study the topology of Lefschetz fibrations by analysing the action of the monodromy on…

We give a maximal set of disjoint $(-1)$-sections of the well-known Lefschetz fibration constructed by Matsumoto, Cadavid and Korkmaz. In fact, we obtain several such sets for a fixed genus, which implies that the Matsumoto-Cadavid-Korkmaz…

The purpose of this note is to explain a combinatorial description of closed smooth oriented 4-manifolds in terms of positive Dehn twist factorizations of surface mapping classes, and further explore these connections. This is obtained via…

Auroux, Donaldson and Katzarkov introduced broken Lefschetz fibrations as a generalization of Lefshcetz fibrations in order to describe near-symplectic 4-manifolds. We first study monodromy representations of higher sides of genus-1…

We consider structures analogous to symplectic Lefschetz pencils in the context of a closed 4-manifold equipped with a `near-symplectic' structure (ie, a closed 2-form which is symplectic outside a union of circles where it vanishes…

We explicitly construct a genus-$3$ Lefschetz fibration over $\mathbb{S}^{2}$ whose total space is $\mathbb{T}^{2}\times \mathbb{S}^{2}\# 6\overline{\mathbb{C} P^{2}}$ using the monodromy of Matsumoto's genus-$2$ Lefschetz fibration. We…

In this article, we characterize isomorphism classes of Lefschetz fibrations with multisections via their monodromy factorizations. We prove that two Lefschetz fibrations with multisections are isomorphic if and only if their monodromy…

In this article, we present a differential topological construction of symplectic Lefschetz pencils of genus $\frac{(d-1)(d-2)}{2}$ with $d^2$ base points and $3(d-1)^2$ critical points for arbitrary $d\geq 4$, analogous to the holomorphic…

We examine the action of the fundamental group $\Gamma$ of a Riemann surface with $m$ punctures on the middle dimensional homology of a regular fiber in a Lefschetz fibration, and describe to what extent this action can be recovered from…

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…

We give a short proof of a conjecture of Stipsicz on the minimality of fiber sums of Lefschetz fibrations, which was proved earlier by Usher. We then construct the first examples of genus g > 1 Lefschetz fibrations on minimal symplectic…

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…

For each g > 2 and h > 1, we explicitly construct (1) fiber sum indecomposable relatively minimal genus g Lefschetz fibrations over genus h surfaces whose monodromies lie in the Torelli group, (2) fiber sum indecomposable genus g surface…

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,…

In this paper we discuss topological properties of holomorphic Lefschetz pencils on the four-torus. Relying on the theory of moduli spaces of polarized abelian surfaces, we first prove that, under some mild assumption, the (smooth)…

We prove an upper bound for the first Betti number of a nontrivial genus-$g$ Lefschetz fibration. We also show that if the monodromy of a Lefschetz fibration is transitive with respect to the mapping class group, the Lefschetz fibration is…