arXiv research

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 of odd spheres' cotangent bundles proven.

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

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 overtwisted structures on elliptic or parabolic torus bundles, this gives a complete …

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

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 conditions. Furthermore, we also demonstrate that every such a minimal symplectic fillin…

Simplified presentation of symplectic fillings of lens spaces.

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

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.

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 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…

New tools classify symplectic fillings of contact 3-manifolds.

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.

Characterizes symplectic rational homology ball fillings of Seifert fibered spaces.

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

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

We prove uniqueness, up to diffeomorphism, of symplectically aspherical fillings of certain unit cotangent bundles, including those of higher-dimensional tori.

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

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

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 …

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…

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…

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 prove that every minimal symplectic filling of the link of a quotient surface singularity can be obtained from its minimal resolution by applying a sequence of rational blow-downs and symplectic antiflips. We present an explicit algorithm inspired by the minimal model program for complex 3-dimensional algebraic vari…

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-…

We describe Lefschetz-Bott fibrations on complex line bundles over symplectic manifolds explicitly. As an application, we construct more than one strong symplectic filling of the link of the $A_{k}$-type singularity. In the appendix, we show that the total space of a Lefschetz-Bott fibration over the unit disk serves a…

The study confirms the non-existence of rational homology ball symplectic fillings for certain Brieskorn spheres.

We prove that any minimal weak symplectic filling of the canonical contact structure on the unit cotangent bundle of a nonorientable closed surface other than the real projective plane is s-cobordant rel boundary to the disk cotangent bundle of the surface. If the nonorientable surface is the Klein bottle, then we show…

The paper explores conditions for homology spheres to bound acyclic smooth manifolds and symplectic fillings.

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…

This paper completely answers the question of when contact (r)-surgery on a Legendrian knot in the standard contact structure on the 3-sphere yields a symplectically fillable contact manifold for r in (0,1]. We also give obstructions for other positive r and investigate Lagrangian fillings of Legendrian knots.

In this survey article we describe different ways of embedding fillings of contact 3-manifolds into closed symplectic 4-manifolds.

In this note we make several observations concerning symplectic cobordisms. Among other things we show that every contact 3-manifold has infinitely many concave symplectic fillings and that all overtwisted contact 3-manifolds are ``symplectic cobordism equivalent.''

Study lens spaces' definite fillings, classifying those with specific inequalities.

The study finds tight contact structures without fillings in high dimensions.

Study monodromy relations in Seifert fibered spaces for 3-manifold fillings.