相关论文: Some applications of Menke's JSJ decomposition for…

We develop a diagrammatic framework for applying the symplectic JSJ decomposition to exact/weak symplectic fillings of 3-dimensional contact manifolds. Namely, we apply the symplectic JSJ decomposition to a contact surgery diagram for some…

We use Menke's JSJ-type decomposition theorem for symplectic fillings to reduce the classification of strong and exact symplectic fillings of virtually overtwisted torus bundles to the same problem for tight lens spaces. For virtually…

We establish a JSJ-type decomposition theorem for splitting exact symplectic fillings of contact 3-manifolds along \emph{mixed tori} -- these are convex tori satisfying a particular geometric condition. As an application, we show that if…

We give finiteness results and some classifications up to diffeomorphism of minimal strong symplectic fillings of Seifert fibered spaces over S^2 satisfying certain conditions, with a fixed natural contact structure. In some cases we can…

We prove that every strong symplectic filling of a planar contact manifold admits a symplectic Lefschetz fibration over the disk, and every strong filling of the 3-torus similarly admits a Lefschetz fibration over the annulus. It follows…

In this paper we give explicit, handle-by-handle constructions of concave symplectic fillings of all closed, oriented contact 3-manifolds. These constructions combine recent results of Giroux relating contact structures and open book…

An important class of contact 3--manifolds are those that arise as links of rational surface singularities with reduced fundamental cycle. We explicitly describe symplectic caps (concave fillings) of such contact 3--manifolds. As an…

We introduce symplectic Calabi-Yau caps to obtain new obstructions to exact fillings. In particular, it implies that any exact filling of the standard unit cotangent bundle of a hyperbolic surface has vanishing first Chern class and has the…

Symplectic fillings of standard tight contact structures on lens spaces are understood and classified. The situation is different if one considers non-standard tight structures (i.e. those that are virtually overtwisted), for which a…

We show that the pre-order defined on the category of contact manifolds by arbitrary symplectic cobordisms is considerably less rigid than its counterparts for exact or Stein cobordisms: in particular, we exhibit large new classes of…

A standard convexity condition on the boundary of a symplectic manifold involves an induced positive contact form (and contact structure) on the boundary; the corresponding concavity condition involves an induced negative contact form. We…

In this paper, we study confoliations in dimensions higher than three mostly from the perspective of symplectic fillability. Our main result is that Massot-Niederkr\"uger-Wendl's bordered Legendrian open book, an object that obstructs the…

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 prove that any weakly symplectically fillable contact manifold is tight. Furthermore we verify the strong Weinstein conjecture for contact manifolds that appear as the concave boundary of a directed symplectic cobordism whose positive…

We consider exact fillings with vanishing first Chern class of asymptotically dynamically convex (ADC) manifolds. We construct two structure maps on the positive symplectic cohomology and prove that they are independent of the filling for…

We show that simply connected contact manifolds that are subcritically Stein fillable have a unique symplectically aspherical filling up to diffeomorphism. Various extensions to manifolds with non-trivial fundamental group are discussed.…

Spinal open book decompositions provide a natural generalization of open book decompositions. We show that any minimal symplectic filling of a contact 3-manifold supported by a planar spinal open book is deformation equivalent to the…

We complete the classification of symplectic fillings of tight contact structures on lens spaces. In particular, we show that any symplectic filling $X$ of a virtually overtwisted contact structure on $L(p,q)$ has another symplectic…

In this second paper of a two-part series, we prove that whenever a contact 3-manifold admits a uniform spinal open book decomposition with planar pages, its (weak, strong and/or exact) symplectic and Stein fillings can be classified up to…

We construct a positive allowable Lefschetz fibration over the disk on any minimal weak symplectic filling of the canonical contact structure on a lens space. Using this construction we prove that any minimal symplectic filling of the…