arXiv research

The paper proves infinitely many strong symplectic fillings for cusp singularity links.

Classifies symplectic fillings of specific torus bundles.

The study describes Lefschetz-Bott fibrations on symplectic manifolds and their applications.

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 prove that all symplectic fillings are obtained by rational blow-downs of a plumbi…

This paper classifies symplectic and Stein fillings of contact 3-manifolds with spinal open book decompositions.

The abstract discusses applications of Menke's JSJ decomposition to symplectic fillings of various 3-manifolds.

Characterizes symplectic rational homology ball fillings of Seifert fibered spaces.

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 same integral homology and intersection form as its disk cotangent bundle. This…

New tools classify symplectic fillings of contact 3-manifolds.

Bourgeois structures are tight in 5D and provide symplectic fillability obstructions.

New examples of tight contact manifolds with algebraic torsion.

New 5D contact manifolds found without fillings or torsion.

We introduce scattering-symplectic manifolds, manifolds with a type of minimally degenerate Poisson structure that is not too restrictive so as to have a large class of examples, yet restrictive enough for standard Poisson invariants to be computable. This paper will demonstrate the potential of the scattering symplect…

Symplectic fillings of prequantization bundles are shown to be disk bundles under certain conditions.

Develops a diagrammatic method for symplectic filling classifications.

The paper classifies symplectic fillings of lens spaces and constructs cobordisms.

The study of symplectic fillings for rational cuspidal curves.

Unique symplectic fillings found for specific cotangent bundles.

The paper classifies minimal symplectic fillings of small Seifert 3-manifolds.

For contact manifolds in dimension three, the notions of weak and strong symplectic fillability and tightness are all known to be inequivalent. We extend these facts to higher dimensions: in particular, we define a natural generalization of weak fillings and prove that it is indeed weaker (at least in dimension five),w…

Unique symplectic fillings of odd spheres' cotangent bundles proven.

Symplectic fillings of surface singularities linked to minimal model program.

Given two open books with equal pages we show the existence of an exact symplectic cobordism whose negative end equals the disjoint union of the contact manifolds associated to the given open books, and whose positive end induces the contact manifold associated to the open book with the same page and concatenated monod…

Study connects lens spaces' fundamental group to their symplectic fillings' second Betti numbers.

Simplified presentation of symplectic fillings of lens spaces.

In this article, using combinatorial techniques of mapping class groups, we show that a Stein fillable integral homology $3$-sphere supported by an open book decomposition with page a $4$-holed sphere admits a unique Stein filling up to diffeomorphism. Furthermore, according to a property of deforming symplectic fillin…

We study symplectic deformation types of minimal symplectic fillings of links of quotient surface singularities. In particular, there are only finitely many symplectic deformation types for each quotient surface singularity.

The paper characterizes symplectic fillings of Seifert 3-manifolds using rational blowdowns.

Study finds symplectic fillings' properties for specific contact covers.

We exhibit tight contact structures on 3-manifolds that do not admit any symplectic fillings.

Study symplectic fillings of sandwiched singularities.

The contact invariant is an element in the monopole Floer homology groups of an oriented closed three manifold canonically associated to a given contact structure. A non-vanishing contact invariant implies that the original contact structure is tight, so understanding its behavior under symplectic cobordisms is of inte…

New proof shows unique symplectic fillings for certain surface singularity links.

New method constructs small symplectic 4-manifolds via contact gluing.

The paper studies symplectic operations on Stein fillings of Brieskorn singularities.

Study symplectic fillings of lens spaces, focusing on virtually overtwisted contact structures.

In this article, we construct a genus-$0$ or genus-$1$ positive allowable Lefschetz fibration on any minimal symplectic filling of the link of non-cyclic quotient surface singularities. As a byproduct, we also show that any minimal symplectic filling of the link of quotient surface singularities can be obtained from a …

In this note we make several observations concerning symplectic fillings. In particular we show that a (strongly or weakly) semi-fillable contact structure is fillable and any filling embeds as a symplectic domain in a closed symplectic manifold. We also relate properties of the open book decomposition of a contact man…

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 canonical contact structure on a lens space is obtained by a sequence of rational blo…

Study shows bounds on symplectic fillings for spinal open book decompositions.

The study finds knots with specific surgeries that don't allow weak symplectic fillings.

The standard contact structure on the three-sphere is invariant under the action of the cyclic group of order p yielding the lens space L(p,q). Therefore, every lens space carries a natural quotient contact structure Q. A theorem of Eliashberg and McDuff classifies the symplectic fillings of (L(p,1), Q) up to diffeomor…

The paper classifies and studies symplectic and contact properties of circular spherical divisors.

We study fillings of contact structures supported by planar open books by analyzing positive factorizations of their monodromy. Our method is based on Wendl's theorem on symplectic fillings of planar open books. We prove that every virtually overtwisted contact structure on L(p,1) has a unique filling, and describe fil…

New invariant connects symplectic fillings and contact structures.

We give examples of contact structures which admit exact symplectic fillings, but no Stein fillings, answering a question of Ghiggini.

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. The proof rests on homological restrictions on symplectic fillings derived from a …

We construct infinitely many Legendrian links in the standard contact $\mathbb{R}^3$ with arbitrarily many topologically distinct Lagrangian fillings. The construction is used to find links in $S^3$ that bound topologically distinct pieces of algebraic curves in $B^4 \subset \mathbb{C}^2$, is applied to find contact 3-…