McDuff–Salamon theory of J-holomorphic curves
E621122
The McDuff–Salamon theory of J-holomorphic curves is a foundational framework in symplectic geometry that systematically develops the analysis, topology, and applications of pseudoholomorphic curves in symplectic manifolds.
All labels observed (2)
| Label | Occurrences |
|---|---|
| J-holomorphic Curves and Symplectic Topology | 1 |
| McDuff–Salamon theory of J-holomorphic curves canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6834194 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: McDuff–Salamon theory of J-holomorphic curves Context triple: [Dusa McDuff, notableWork, McDuff–Salamon theory of J-holomorphic curves]
-
A.
The geometry of four-manifolds
The Geometry of Four-Manifolds is a foundational monograph in differential geometry that develops the theory of smooth four-dimensional manifolds using gauge theory and Yang–Mills instantons.
-
B.
Topological Methods in Algebraic Geometry
Topological Methods in Algebraic Geometry is a foundational mathematical monograph by Friedrich Hirzebruch that applies topological techniques, particularly characteristic classes and cobordism theory, to problems in algebraic geometry.
-
C.
Lefschetz fibration
A Lefschetz fibration is a smooth map from a higher-dimensional manifold to a lower-dimensional one whose singularities are modeled on complex Morse-type critical points, playing a central role in symplectic and complex geometry.
-
D.
Differential Analysis on Complex Manifolds
"Differential Analysis on Complex Manifolds" is a foundational mathematical monograph that systematically develops the theory of differential and complex geometry on complex manifolds.
-
E.
Singular Points of Complex Hypersurfaces
"Singular Points of Complex Hypersurfaces" is a foundational monograph in singularity theory that systematically studies the local and topological properties of singularities arising in complex algebraic and analytic hypersurfaces.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: McDuff–Salamon theory of J-holomorphic curves Target entity description: The McDuff–Salamon theory of J-holomorphic curves is a foundational framework in symplectic geometry that systematically develops the analysis, topology, and applications of pseudoholomorphic curves in symplectic manifolds.
-
A.
The geometry of four-manifolds
The Geometry of Four-Manifolds is a foundational monograph in differential geometry that develops the theory of smooth four-dimensional manifolds using gauge theory and Yang–Mills instantons.
-
B.
Topological Methods in Algebraic Geometry
Topological Methods in Algebraic Geometry is a foundational mathematical monograph by Friedrich Hirzebruch that applies topological techniques, particularly characteristic classes and cobordism theory, to problems in algebraic geometry.
-
C.
Lefschetz fibration
A Lefschetz fibration is a smooth map from a higher-dimensional manifold to a lower-dimensional one whose singularities are modeled on complex Morse-type critical points, playing a central role in symplectic and complex geometry.
-
D.
Differential Analysis on Complex Manifolds
"Differential Analysis on Complex Manifolds" is a foundational mathematical monograph that systematically develops the theory of differential and complex geometry on complex manifolds.
-
E.
Singular Points of Complex Hypersurfaces
"Singular Points of Complex Hypersurfaces" is a foundational monograph in singularity theory that systematically studies the local and topological properties of singularities arising in complex algebraic and analytic hypersurfaces.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
framework for pseudoholomorphic curves
ⓘ
mathematical theory ⓘ theory in symplectic geometry ⓘ |
| appliesTo | symplectic manifolds ⓘ |
| associatedWith |
Dietmar Salamon
NERFINISHED
ⓘ
Dusa McDuff NERFINISHED ⓘ |
| buildsOn | Gromov theory of pseudoholomorphic curves NERFINISHED ⓘ |
| clarifies |
analytic foundations of pseudoholomorphic curve theory
ⓘ
compactness and bubbling phenomena ⓘ transversality and regularity issues ⓘ |
| contributesTo |
Floer theory
NERFINISHED
ⓘ
construction of Gromov–Witten invariants ⓘ foundations of symplectic topology NERFINISHED ⓘ |
| develops |
analysis of J-holomorphic curves
ⓘ
applications of J-holomorphic curves ⓘ topology of J-holomorphic curves ⓘ |
| documentedIn |
Introduction to Symplectic Topology
NERFINISHED
ⓘ
J-holomorphic Curves and Symplectic Topology NERFINISHED ⓘ |
| emphasizes |
Fredholm setup for Cauchy–Riemann operators
ⓘ
gluing constructions for curves ⓘ orientation of moduli spaces ⓘ |
| field | symplectic geometry ⓘ |
| focusesOn |
J-holomorphic curves
ⓘ
pseudoholomorphic curves ⓘ |
| frameworkFor | systematic study of J-holomorphic curves in symplectic manifolds ⓘ |
| providesToolsFor |
Gromov–Witten theory
NERFINISHED
ⓘ
Hamiltonian dynamics ⓘ symplectic topology ⓘ |
| studies |
holomorphic curves in almost complex manifolds
ⓘ
intersection theory in symplectic manifolds ⓘ moduli spaces of pseudoholomorphic curves ⓘ symplectic invariants ⓘ |
| usedFor |
defining invariants of symplectic manifolds
ⓘ
proving symplectic non-squeezing results ⓘ studying Hamiltonian periodic orbits ⓘ studying symplectic embeddings ⓘ |
| usesConcept |
Fredholm theory
NERFINISHED
ⓘ
Gromov compactness NERFINISHED ⓘ almost complex structures ⓘ bubbling analysis ⓘ compactness theorems ⓘ compatible almost complex structures ⓘ elliptic regularity ⓘ energy estimates ⓘ moduli spaces of curves ⓘ tame almost complex structures ⓘ transversality ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: McDuff–Salamon theory of J-holomorphic curves Description of subject: The McDuff–Salamon theory of J-holomorphic curves is a foundational framework in symplectic geometry that systematically develops the analysis, topology, and applications of pseudoholomorphic curves in symplectic manifolds.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
J-holomorphic Curves and Symplectic Topology