arXiv research

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.

Symplectic embeddings of balls into specific manifolds are studied, with restrictions and obstructions identified.

Study realizes symplectic algebras and homotopy types on manifolds.

Inequalities for symplectic cohomology groups are derived.

New flows introduced for symplectic geometry.

Study of Type IIA flow on symplectic Lie algebras for geometric structures.

Characterizes density-valued symplectic forms on multisymplectic manifolds.

We introduce symplectic structures on "Lie pairs" of (real or complex) algebroids as studied by Chen, Stienon and the second author (From Atiyah classes to homotopy Leibniz algebras, arXiv:1204.1075), encompassing homogeneous symplectic spaces, symplectic manifolds with a $\mathfrak g$-action and holomorphic symplectic…

Given the Euclidean space $\R^{2n+2}$ endowed with a constant symplectic structure and the standard flat connection, and given a polynomial of degree 2 on that space, Baguis and Cahen have defined a reduction procedure which yields a symplectic manifold endowed with a Ricci-type connection. We observe that any symplect…

Proves a vanishing property for symplectic manifold cohomology.

Convexity theorem for Hamiltonian actions on conformal symplectic manifolds.

Construct symplectic Lefschetz fibrations with any signature and spin type.

Study preserves symplectic structure in forced discrete mechanical systems.

The Type IIA flow converges on symplectic manifolds, with singularity models identified.

The paper explores complex geometries of 3-forms on symplectic 6-manifolds.

Extends AKSZ to poly-symplectic structures for more complex spaces.

This paper establishes a correspondence between Einstein-Hermitian metrics and stability for generalized holomorphic vector bundles over symplectic type generalized Kahler manifolds.

Ancient solutions found for a specific flow on symplectic half-flat structures.

Real Lagrangians in toric manifolds are classified by combinatorial data.

We study the holomorphic symplectic structures on hyper-Kaehler manifolds of type A_{\infty}, by using the torus action.

This paper provides a new method to construct $b$-symplectic toric manifolds from toric manifolds.

Symplectic Torelli groups of positive rational surfaces are trivial or sphere braid groups.

Existence of symplectic structure shown on Seiberg-Witten moduli space product of Riemann surfaces.

Develops a correspondence between symplectic orbits and Grassmannians.

We present a simple explicit construction of hyper-Kaehler and hyper-symplectic (also known as neutral hyper-Kaehler or hyper-parakaehler) metrics in 4D using the Bianchi type groups of class A. The construction underlies a correspondence between hyper-Kaehler and hyper-symplectic structures in dimension four.

First steps towards a classification of irreducible symplectic 4-folds whose integral 2-cohomology with 4-tuple cup product is isomorphic to that of Hilb^2(K3). We prove that any such 4-fold deforms to an irreducible symplectic 4-fold of Type A or Type B. A 4-fold of Type A is a double cover of a (singular) sextic hype…

The moduli space of Higgs bundles is stratified into complex symplectic submanifolds.

We compute the homotopy type of the space of T^n-equivariant symplectic embeddings from the standard 2n-dimensional ball of some fixed radius into a 2n-dimensional symplectic-toric manifold M, and use this computation to define a Z-valued step function on the positive real line which is an invariant of the symplectic-t…

Study on symplectic Dirac operators on foliations, estimating eigenvalues.

Stability of Type IIA flow ensures Kähler properties of Calabi-Yau 3-folds.

Unique symplectic fillings found for specific cotangent bundles.

Symplectic classification for a specific type of singularity in integrable systems.

Geometric flow on symplectic manifolds connects to Type IIA string theory.

We introduce the cutting construction of possibly non-compact symplectic toric manifolds, in particular, toric symplectic cones that correspond to a weakly convex good cone. Since the symplectization of a toric contact manifold is a toric symplectic cone, we can also construct toric contact manifolds that correspond to…

We consider invariant symplectic connections $\nabla$ on homogeneous symplectic manifolds $(M,ω)$ with curvature of Ricci type. Such connections are solutions of a variational problem studied by Bourgeois and Cahen, and provide an integrable almost complex structure on the bundle of almost complex structures compatible…

Solves Calabi-Yau equation on symplectic manifolds using measurable Kahler metrics.

We give an elementary construction of symplectic connections through reduction. This provides an elegant description of a class of symmetric spaces and gives examples of symplectic connections with Ricci type curvature, which are not locally symmetric; the existence of such symplectic connections was unknown.

We consider analytic curves $\nabla^t$ of symplectic connections of Ricci type on the torus $T^{2n}$ with $\nabla^0$ the standard connection. We show, by a recursion argument, that if $\nabla^t$ is a formal curve of such connections then there exists a formal curve of symplectomorphisms $ψ_t$ such that $ψ_t\cdot\nabla^…

Stabilized convex symplectic manifolds are equivalent to flexible Weinstein manifolds.

Study on contact type hypersurfaces in 4-space, proving no Brieskorn spheres can embed.

We introduce Morse-type inequalities for a holomorphic circle action on a holomorphic vector bundle over a compact Kaehler manifold. Our inequalities produce bounds on the multiplicities of weights occurring in the twisted Dolbeault cohomology in terms of the data of the fixed points and of the symplectic reduction. Th…

Unique symplectic fillings of odd spheres' cotangent bundles proven.

New symplectic barriers found in ball embeddings.

Paper constructs an invariant for a specific type of complex manifolds.

This article is an overview of the results obtained in recent years on symplectic connections. We present what is known about preferred connections (critical points of a variational principle). The class of Ricci-type connections (for which the curvature is entirely determined by the Ricci tensor) is described in detai…

Study on types of generalized hypercomplex structures on tori and Kodaira-Thurston surface.

Estimates symplectic Calabi-Yau equation using Cheng-Yau method.

We give examples of compact symplectic manifolds with disconnected contact type boundary in dimension $4n$ for any $n\geq 1$. The example is given by a subset of the tangent bundle of a compact quotient of the complex hyperbolic space endowed with the canonical symplectic form plus a generalized magnetic field and its …