arXiv research

Study on mean Euler characteristic of Gorenstein toric contact manifolds.

A Calabi-Yau orbifold is locally modeled on C^n/G where G is a finite subgroup of SL(n, C). In dimension n=3 a crepant resolution is given by Nakamura's G-Hilbert scheme. This crepant resolution has a description as a GIT/symplectic quotient. We use tools from global analysis to give a geometrical generalization of the…

New method recovers hyperkähler metrics from twistor models.

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.

Classifies symplectic fillings of specific torus bundles.

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.

Unique symplectic fillings of odd spheres' cotangent bundles proven.

Given an integer b and a finitely presented group G we produce a compact symplectic six-manifold with c_1 = 0, b_2 > b, b_3 > b and fundamental group G. In the simply-connected case we can also arrange for b_3 = 0; in particular these examples are not diffeomorphic to Kähler manifolds with c_1 = 0. The construction beg…

Let S be a K3 surface that admits a non-symplectic automorphism $ρ$ of order 3. We divide $S\times \mathbb{P}^1$ by $ρ\timesψ$ where $ψ$ is an automorphism of order 3 of $\mathbb{P}^1$. There exists a threefold ramified cover of a partial crepant resolution of the quotient that is a Calabi-Yau orbifold. We compute the …

Symplectic fillings of surface singularities linked to minimal model program.

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

The study creates Lefschetz fibrations for symplectic fillings of specific surface singularities.

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

Simplified presentation of symplectic fillings of lens spaces.

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

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.

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.

Study symplectic fillings of sandwiched singularities.

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

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

The paper solves when surgeries on Legendrian knots yield symplectically fillable contact manifolds.

Characterizes symplectic rational homology ball fillings of Seifert fibered spaces.

The paper constructs Ricci-flat Kähler manifolds with specific decay properties.

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

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

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 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.

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 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.

New geometric constructions for contact manifolds, not symplectically fillable.

Existence of solitons on resolved finite quotient spaces.

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-…