Related papers: Generalized Chain Surgeries and Applications
Exploiting the affinity between stable generalized complex structures and symplectic structures, we explain how certain constructions coming from symplectic geometry can be performed in the generalized complex setting. We introduce…
Applying logarithmic transformations along 2-tori, we construct a generalized complex structure J_n with n type changing luci for every $n\geq 0$ on genus 1-Lefschetz fibrations with a cusp neighborhood, which include elliptic surfaces with…
We introduce blow-up and blow-down operations for generalized complex 4-manifolds. Combining these with a surgery analogous to the logarithmic transform, we then construct generalized complex structures on nCP2 # m \bar{CP2} for n odd, a…
A symplectic rational cuspidal curve with positive self-intersection number admits a concave neighborhood, and thus a corresponding contact manifold on the boundary. In this article, we study symplectic fillings of such contact manifolds,…
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…
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 define symplectic fractional twists, which generalize Dehn twists, and use these in open books to investigate contact structures. The resulting contact structures are invariant under a circle action, and share several similarities with…
We consider certain type of fiber bundles with odd dimensional compact contact base, exact symplectic fibers, and the structure group contained in the group of exact symplectomorphisms of the fiber. We call such fibrations "contact…
In this paper, we investigate the minimal symplectic fillings of small Seifert 3-manifolds with a canonical contact structure. As a result, we classify all minimal symplectic fillings of small Seifert 3-manifolds satisfying certain…
We discuss and prove a number of cohomological results for Milnor fibers, real links, and complex links of local complete intersections with singularities of arbitrary dimension.
We discuss the interplay between lagrangian distributions and connections in symplectic geometry, beginning with the traditional case of symplectic manifolds and then passing to the more general context of poly- and multisymplectic…
We study elliptic fibrations by analyzing suitable deformations of the fibrations and vanishing cycles. We introduce geometric string junctions and describe some of their properties. We show how the structure of the geometric string…
In this paper we compute in some new cases the cardinalities of the fibers of certain natural fibrations that appear in the analysis of the configuration space of the Heisenberg ring. This is done by means of certain cyclic group actions on…
A classical and beautiful story in geometric representation theory is the construction by Springer of an action of the Weyl group on the cohomology of the fibres of the Springer resolution of the nilpotent cone. We establish a natural…
We apply Menke's JSJ decomposition for symplectic fillings to several families of contact 3-manifolds. Among other results, we complete the classification up to orientation-preserving diffeomorphism of strong symplectic fillings of lens…
This article describes a normal form algorithm for the Brieskorn lattice of an isolated hypersurface singularity. It is the basis of efficient algorithms to compute the Bernstein-Sato polynomial, the complex monodromy, and Hodge-theoretic…
In this article we study Lefschetz fibration structures on knot surgery 4-manifolds obtained from an elliptic surface E(2) using Kanenobu knots $K$. As a result, we get an infinite family of simply connected mutually diffeomorphic…
Infinitely many contact 3-manifolds each admitting infinitely many, pairwise non-diffeomorphic Stein fillings are constructed. We use Lefschetz fibrations in our constructions and compute their first homologies to distinguish the fillings.
In this article we use the technique of Luttinger surgery to produce small examples of simply connected and non-simply connected minimal symplectic 4-manifolds. In particular, we construct: (1) An example of a minimal symplectic 4-manifold…
Let A be an affine variety inside a complex N dimensional vector space which has an isolated singularity at the origin. The intersection of A with a very small sphere turns out to be a contact manifold called the link of A. Any contact…