Related papers: On 4-Manifolds, Folds and Cusps

It is known that an arbitrary smooth, oriented 4-manifold admits the structure of what is called a broken Lefschetz fibration. Given a broken fibration, there are certain modifications, realized as homotopies of the fibration map, that…

We construct noncomplex smooth 4-manifolds which admit genus-2 Lefschetz fibrations over S^2. The fibrations are necessarily hyperelliptic, and the resulting 4-manifolds are not even homotopy equivalent to complex surfaces. Furthermore,…

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…

In this paper we study colored triangulations of compact PL 4-manifolds with empty or connected boundary which induce handle decompositions lacking in 1-handles or in 1- and 3-handles, thus facing also the problem, posed by Kirby, of the…

We study lines and twisted cubics on cubic fourfolds with simple isolated singularities. We show that the Hilbert scheme compactification of the total space of Starr's fibration on the space of twisted cubics on a cubic fourfold with simple…

We show that only finitely many links in a closed 3-manifold share the same complement, up to twists along discs and annuli. Using the same techniques, we prove that by adding 2-handles on the same link we get only finitely many smooth…

This note presents the handlebody argument for modifying achiral Lefschetz singularities into broken Lefschetz fibrations, yielding a handlebody proof of the existence of broken Lefschetz fibrations on arbitrary closed smooth oriented…

Bryant-Salamon constructed three 1-parameter families of complete manifolds with holonomy $\mathrm{G}_2$ which are asymptotically conical to a holonomy $\mathrm{G}_2$ cone. For each of these families, including their asymptotic cone, we…

In this article we show that every closed oriented smooth 4-manifold can be decomposed into two codimension zero submanifolds (one with reversed orientation) so that both pieces are exact Kahler manifolds with strictly pseudoconvex…

We use symplectic cohomology to study the non-uniqueness of symplectic structures on the smooth manifolds underlying affine varieties. Starting with a Lefschetz fibration on such a variety and a finite set of primes, the main new tool is a…

The topology of Stein surfaces and contact 3-manifolds is studied by means of handle decompositions. A simple characterization of homeomorphism types of Stein surfaces is obtained --- they correspond to open handlebodies with all handles of…

In a pair of papers, we construct invariants for smooth four-manifolds equipped with `broken fibrations' - the singular Lefschetz fibrations of Auroux, Donaldson and Katzarkov - generalising the Donaldson-Smith invariants for Lefschetz…

Using the existence of certain symplectic submanifolds in symplectic 4-manifolds, we prove an estimate from above for the number of singular fibers with separating vanishing cycles in minimal Lefschetz fibrations over surfaces of positive…

We construct examples of Lefschetz fibrations with prescribed singular fibers. By taking differences of pairs of such fibrations with the same singular fibers, we obtain new examples of surface bundles over surfaces with non-zero signature.…

The complement of a complexified real line arrangement is an affine surface. It is classically known that such a space has a handle decomposition up to $2$-handles. We will describe the handle decomposition induced from Lefschetz hyperplane…

We show that any 4-manifold, after surgery on a curve, admits an achiral Lefschetz fibration. In particular, we show that the connected sum of any simply connected 4-manifold with a 2-sphere bundle over the 2-sphere will admit an achiral…

Soft elastic sheets resting on rigid surfaces develop wrinkles, rucks, and folds due to the combined influence of elasticity, gravity, and contact interactions. Despite their ubiquity, the principles governing their morphology and…

This is a summary of some of the basic facts about flat 2-orbifold groups, otherwise known as 2-dimensional crystallographic groups. We relate the geometric and topological presentations of these groups, and consider structures…

A simplified trisection is a trisection map on a 4-manifold such that, in its critical value set, there is no double point and cusps only appear in triples on innermost fold circles. We give a necessary and sufficient condition for a…

We show that every smooth, closed, orientable 4-manifold X admits a special kind of handlebody decomposition that we call horizontal. We classify the closed 4-manifolds with the simplest horizontal decompositions and we describe all such…