New differential complexes on symplectic manifolds.
problem Developing calculus on symplectic manifolds.
method Coupling a symplectic manifold to a vector bundle with a constrained curvature.
result Construction of new differential complexes.
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48 results for “complex symplectic manifolds”
Study on symplectic structures and their deformations.
problem Preservation of complex symplectic structures under deformations.
method Analyzes various cohomologies and conditions for deformations.
result Obtains topological obstructions for compact complex symplectic manifolds.
The study provides obstructions and examples for -symplectic structures on complex manifolds.
problem Obstructing the existence of -symplectic structures on compact complex manifolds.
method Analyzing properties of -transverse forms and -forms.
result Found obstructions and examples of -symplectic structures on compact complex manifolds.
Symplectic structures simplified for compact manifolds.
problem Locally conformally symplectic structures on compact manifolds.
method Symplectic analogue of Vaisman's theorem.
result Locally conformally symplectic structures become globally symplectic.
The paper explores spaces of Kähler and symplectic forms on 4-manifolds.
problem Investigating the properties of Kähler and symplectic forms on 4-manifolds.
method Analyzing the uniqueness, connectedness, and openness of spaces of Kähler forms and introducing holomorphically tamed symplectic forms.
result Formulated a parallel question for holomorphically tamed symplectic forms and related it to Kähler-type symplectic forms.
Classifies complex symplectic structures on Lie algebras with large abelian ideals.
problem Classifying complex symplectic structures on Lie algebras with large abelian ideals.
method Two constructions of complex symplectic structures on Lie algebras with large abelian ideals, considering compact quotients of Lie groups.
result Complete classification of complex symplectic structures on almost abelian Lie algebras.
The abstract proves a Moser-like theorem for C-symplectic structures and applies it to complex manifolds.
problem Analyzing the isotopy of C-symplectic structures and their applications.
method Proves an analogue of Moser's isotopy theorem for families of C-symplectic structures.
result Locally trivial degenerate twistorial deformation over the base of holomorphic Lagrangian fibrations.
Study symplectic 4-manifolds with using Luttinger surgery.
problem Complexity of fundamental groups in symplectic 4-manifolds with .
method Luttinger surgery technique applied to symplectic 4-manifolds.
result Various constructions of symplectic 4-manifolds with .
New symplectic 4-manifolds with non-negative signatures are constructed using complex surfaces and quotients.
problem Creating new symplectic 4-manifolds with non-negative signatures.
method Using complex surfaces, Cartwright-Steger surfaces, and Hirzebruch's line-arrangement surfaces, along with quotients.
result Irreducible symplectic and non-symplectic 4-manifolds homeomorphic but not diffeomorphic to are constructed.
Study of special almost complex structures on symplectic manifolds.
problem Understanding special almost complex structures on symplectic manifolds.
method Examined homogeneous compatible almost complex structures, focusing on those with Chern-Ricci form being a multiple of the symplectic form.
result Compact isotropy co-adjoint orbits of semi-simple Lie groups admit special compatible almost complex structures under certain conditions.
Lagrangian branes with boundary and symplectic methods for stable generalized complex manifoldsmath.DG
This paper introduces new Lagrangian branes in stable generalized complex manifolds.
problem Understanding stable generalized complex manifolds and their properties.
method Using log symplectic geometry and Floer theory techniques.
result Lagrangian branes with boundary are introduced and their properties are studied.
The paper extends a result about circle actions on symplectic manifolds to almost complex manifolds.
problem Understanding circle actions on almost complex manifolds with isolated fixed points.
method Analyzes the conditions for circle actions on compact, connected almost complex manifolds with exactly three fixed points.
result If a circle acts on a compact, connected almost complex manifold with exactly three fixed points, the manifold is equivariantly symplectomorphic to .
The paper classifies minimal symplectic fillings of small Seifert 3-manifolds.
problem Classifying minimal symplectic fillings of small Seifert 3-manifolds.
method Using rational blowdowns and weighted homogeneous complex surface singularities.
result Every minimal symplectic filling of small Seifert 3-manifolds is obtained by a sequence of rational blowdowns.
Special complex manifoldsmath.DG
We introduce the notion of a special complex manifold: a complex manifold (M,J) with a flat torsionfree connection \nabla such that (\nabla J) is symmetric. A special symplectic manifold is then defined as a special complex manifold together with a \nabla-parallel symplectic form ω. This generalises Freed's definition …
We introduce certain homology and cohomology subgroups for any almost complex structure and study their pureness, fullness and duality properties. Motivated by a question of Donaldson, we use these groups to relate J-tamed symplectic cones and J-compatible symplectic cones over a large class of almost complex manifolds…
Stabilized convex symplectic manifolds are equivalent to flexible Weinstein manifolds.
problem Understanding the equivalence between stabilized convex symplectic manifolds and flexible Weinstein manifolds.
method Analyzing the homotopy type and symplectic properties of the manifolds.
result Stabilized convex symplectic manifolds are symplectomorphic to flexible Weinstein manifolds.
New symplectic caps and embeddings found in complex projective plane.
problem Embeddings of homology balls in complex projective plane.
method Handlebody construction of symplectic caps and embeddings.
result First examples of symplectic handlebody decompositions of a closed symplectic 4-manifold.
For a symplectic manifold admitting a metaplectic structure (a symplectic analogue of the Riemannian spin structure), we construct a sequence consisting of differential operators using a symplectic torsion-free affine connection. All but one of these operators are of first order. The first order ones are symplectic ana…
The study examines cohomological aspects on complex and symplectic manifolds.
problem Understanding qualitative properties through quantitative cohomological information.
method Analysis of Bott-Chern and Aeppli cohomology groups.
result Established comparisons among cohomology group dimensions and proved the -lemma and Hard-Lefschetz condition.
Solves Calabi-Yau equation on symplectic manifolds using measurable Kahler metrics.
problem Solving the Calabi-Yau equation on symplectic manifolds.
method Global deformation of almost complex structures compatible with symplectic form, constructing measurable Lipschitz Kahler metric.
result Existence theorem for solutions to the one-form type Calabi-Yau equation on closed symplectic manifolds.
Positivity of intersections in 4-manifolds leads to taming symplectic structures.
problem Taming symplectic structures in almost complex 4-manifolds.
method Proof of positivity of intersections of pseudoholomorphic curves.
result Positivity of intersections is stable and leads to taming symplectic structures.
New symplectic forms derived from Lagrangian fibrations on symplectic manifolds.
problem Deriving new symplectic forms from existing ones.
method Proving existence of degenerate twistorial deformations.
result Existence of degenerate twistorial deformations preserving complex structures.
New symplectic structures found on complex manifolds without Kähler structures.
problem Finding symplectic structures on complex manifolds without Kähler structures.
method Constructing explicit lattices and cohomological computations.
result Compact complex manifolds with symplectic structures satisfying the Hard Lefschetz Condition.
We introduce a surgery for generalized complex manifolds whose input is a symplectic 4-manifold containing a symplectic 2-torus with trivial normal bundle and whose output is a 4-manifold endowed with a generalized complex structure exhibiting type change along a 2-torus. Performing this surgery on a K3 surface, we obt…
New calculations of topological complexity for symplectic CW-complexes.
problem Calculating topological complexity for symplectic CW-complexes.
method Using atoroidal cohomology classes and CW-complexes, proving topological complexity for symplectic spaces.
result Every atoroidally symplectic CW-complex of dimension 2n has topological complexity 4n.
Holomorphic symplectic structure on Lagrangian moduli space.
problem Understanding the structure of Lagrangian submanifolds in hyperKähler manifolds.
method Proving the existence of a natural holomorphic symplectic structure on the relative Albanese over the moduli space.
result The relative Albanese over the moduli space of complex Lagrangian submanifolds has a natural holomorphic symplectic structure.
Symplectic Rational Blow-upmath.SG
Fintushel and Stern defined the rational blow-down construction [FS] for smooth 4-manifolds, where a linear plumbing configuration of spheres is replaced with a rational homology ball , . Subsequently, Symington [Sy] defined this procedure in the symplectic category, where a symplectic (given…
Study Kodaira dimensions on almost complex manifolds, proving integrability and structural descriptions.
problem Understanding Kodaira dimensions on almost complex manifolds.
method Using pseudoholomorphic pluricanonical maps, defining new dimensions, and applying probabilistic combinatorics.
result Almost complex structures with top Kodaira dimension are integrable, and for compact 4-manifolds, they have elliptic fibration structures.
Introduces symplectic flatness for connections over symplectic manifolds.
problem Flatness conditions for connections over symplectic manifolds.
method Introduces symplectic flatness condition and twisting of differential complexes.
result Symplectic flat connections represent a subclass of Yang-Mills connections.
Study isotopy of rational cuspidal curves in 4-manifolds.
problem Isotopy of rational cuspidal curves in 4-manifolds.
method Tame symplectic curves, pseudo-holomorphic curves, log pairs, 4-dimensional topology.
result Every rational cuspidal curve is isotopic to a complex curve in degrees up to 5.
The study constructs symplectic 4-manifolds with exotic structures.
problem Creating symplectic 4-manifolds with exotic smooth structures.
method Using star surgeries and complex singularities, the study constructs these manifolds.
result Symplectic 4-manifolds with one Seiberg-Witten basic class are constructed.
The study confirms Gromov's speculation and provides bounds for taming symplectic structures.
problem Understanding the relationship between taming symplectic structures and the area of pseudoholomorphic curves.
method Analyzes the numerical cone of taming symplectic structures and characterizes coarsely holomorphic curves.
result An almost complex manifold with an area bound admits a taming symplectic structure, confirming Gromov's speculation.
Proves a vanishing property for symplectic manifold cohomology.
problem Generalizing complex geometry results to symplectic geometry.
method Based on Tseng and Zhou's vanishing property under symplectic flatness.
result Establishes necessity of symplectic flatness for certain results.
Generalized complex structures on certain torus bundles are explored.
problem Exploring generalized complex structures on specific torus bundles.
method Analyzing principal torus bundles over complex manifolds with even dimensional fibers and characteristic class of type (1,1).
result Generalized complex structures on these bundles are equivalent to products of complex and symplectic structures in tubular neighborhoods of fibers.
Classifies symplectic torus actions up to equivariant symplectomorphism.
problem Classifying symplectic torus actions up to equivariant symplectomorphism.
method Classification theorems based on Duistermaat and Pelayo's work on symplectic torus actions with coisotropic orbits.
result Every almost isotropy-maximal symplectic torus action is equivariantly diffeomorphic to a product of a symplectic toric manifold and a torus.
On a smooth manifold M, generalized complex (generalized paracomplex) structures provide a notion of interpolation between complex (paracomplex) and symplectic structures on M. Given a complex manifold (M,j), we define six families of distinguished generalized complex or paracomplex structures on M. Each one of them in…
Introduces a Morse complex on symplectic manifolds using gradient flows and proves its cohomology is independent of metrics and Morse functions.
problem Cohomology of symplectic manifolds under different metrics and Morse functions.
method Symplectic Morse complex with gradient flows and Witten deformation.
result Cohomology of the complex is isomorphic to Tsai, Tseng, and Yau's cohomology and independent of metrics and Morse functions.
An -algebra is built on symplectic manifold homology.
problem No specific problem stated; focuses on construction of algebra.
method Construction of an -algebra on symplectic manifold homology.
result The constructed -algebra naturally projects to a Lie algebra extension.
Study cohomology of almost complex and symplectic manifolds under proper maps.
problem Understand cohomology relationships in almost-complex and symplectic settings.
method Analyze cohomology groups of de Rham cohomology and pseudo-holomorphic maps.
result Provide new characterizations and relationships in cohomology groups.
Study on smooth moduli spaces of branes in symplectic 4-manifolds.
problem Understanding the moduli spaces of spacefilling branes in symplectic 4-manifolds.
method Used the local Torelli theorem for K3 surfaces and tori to prove the smoothness of the moduli space.
result Determined the dimension of the moduli space of spacefilling branes.
The paper examines symplectic structures and their relation to the partial derivative lemma.
problem Understanding the relationship between complex symplectic structures and the partial derivative lemma.
method Analyzes complex symplectic manifolds and their associated Beauville-Bogomolov-Fujiki quadric.
result The quadric is smooth if and only if and irreducible if and only if when the partial derivative lemma holds.
The study describes Lefschetz-Bott fibrations on symplectic manifolds and their applications.
problem Understanding Lefschetz-Bott fibrations on symplectic manifolds.
method Explicit construction and analysis of Lefschetz-Bott fibrations over line bundles.
result Construction of strong symplectic fillings of symplectic manifolds.
The harmonic cohomology of a Donaldson symplectic submanifold and of an Auroux symplectic submanifold are compared with that of its ambient space. We also study symplectic manifolds satisfying a weakly Lefschetz property, that is, the -Lefschetz propery. In particular, we consider the symplectic blow-ups of the comp…
The study classifies complex symplectic structures on 4D Lie algebras and constructs hypersymplectic structures.
problem Classifying and constructing complex symplectic structures on 4D Lie algebras.
method Interpreting complex symplectic and pseudo-Kähler structures, developing a method for constructing hypersymplectic structures.
result Obtained an example of a hypersymplectic structure on a 4-step nilmanifold.
Let M be a 4-manifold which admits a free circle action. We use twisted Alexander polynomials to study the existence of symplectic structures and the minimal complexity of surfaces in M. The results on the existence of symplectic structures summarize previous results of the authors in [FV08a,FV08,FV07]. The results on …
Study cohomologies of complex manifolds with symplectic forms and their stability.
problem Analyzing cohomologies of complex manifolds with symplectic forms.
method Investigate the Hard Lefschetz Condition on Dolbeault cohomology groups using a double complex.
result Stability of the -Lemma under small deformations of but not under complex structure.
The paper proves symplectic forms on tamed almost complex 4-manifolds.
problem Finding symplectic forms on tamed almost complex 4-manifolds.
method Unified proof approach similar to Buchdahl's Kodaira conjecture proof.
result Existence of new symplectic forms compatible with given almost complex structure.
The paper establishes criteria for symplectic surfaces in 4-manifolds.
problem Finding symplectic surfaces in 4-manifolds with bounded genus.
method Criterion for minimization of genus among surfaces with given homology and boundary.
result Symplectic surfaces minimize slice genus for their boundary in contact 3-manifolds.