Introduction to Symplectic Topology
E621124
Introduction to Symplectic Topology is a foundational graduate-level textbook that systematically develops the theory and applications of symplectic manifolds and symplectic geometry.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Introduction to Symplectic Topology canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6834197 — 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: Introduction to Symplectic Topology Context triple: [Dusa McDuff, authorOf, Introduction to Symplectic Topology]
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A.
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.
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B.
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.
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C.
Morse Theory
Morse Theory is a branch of differential topology that studies the relationship between the topology of manifolds and the critical points of smooth real-valued functions defined on them.
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D.
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.
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E.
Liouville–Arnold theorem
The Liouville–Arnold theorem is a fundamental result in Hamiltonian mechanics that guarantees the integrability of a system with sufficiently many conserved quantities and describes its motion as quasi-periodic on invariant tori in phase space.
- 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: Introduction to Symplectic Topology Target entity description: Introduction to Symplectic Topology is a foundational graduate-level textbook that systematically develops the theory and applications of symplectic manifolds and symplectic geometry.
-
A.
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.
-
B.
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.
-
C.
Morse Theory
Morse Theory is a branch of differential topology that studies the relationship between the topology of manifolds and the critical points of smooth real-valued functions defined on them.
-
D.
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.
-
E.
Liouville–Arnold theorem
The Liouville–Arnold theorem is a fundamental result in Hamiltonian mechanics that guarantees the integrability of a system with sufficiently many conserved quantities and describes its motion as quasi-periodic on invariant tori in phase space.
- F. None of above. chosen
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
mathematics book
ⓘ
textbook ⓘ |
| author |
Dietmar Salamon
NERFINISHED
ⓘ
Dusa McDuff NERFINISHED ⓘ |
| contains |
examples
ⓘ
exercises ⓘ historical notes ⓘ |
| countryOfPublication | United Kingdom ⓘ |
| field |
differential geometry
ⓘ
symplectic geometry ⓘ symplectic topology ⓘ topology ⓘ |
| firstEditionPublicationYear | 1995 ⓘ |
| hasEdition |
first edition
ⓘ
second edition ⓘ third edition ⓘ |
| hasFormat |
ebook
ⓘ
hardcover ⓘ paperback ⓘ |
| isWidelyUsedAs |
course textbook in symplectic geometry
ⓘ
standard reference in symplectic topology ⓘ |
| language | English ⓘ |
| level | graduate ⓘ |
| publisher | Oxford University Press ⓘ |
| secondEditionPublicationYear | 1998 ⓘ |
| series | Oxford Mathematical Monographs NERFINISHED ⓘ |
| targetAudience |
graduate students in mathematics
ⓘ
researchers in symplectic geometry ⓘ |
| thirdEditionPublicationYear | 2017 ⓘ |
| topic |
Darboux theorem
NERFINISHED
ⓘ
Floer homology NERFINISHED ⓘ Gromov–Witten invariants NERFINISHED ⓘ Hamiltonian dynamics ⓘ Hamiltonian group actions ⓘ J-holomorphic curves ⓘ Lagrangian submanifolds ⓘ Moser’s stability theorem NERFINISHED ⓘ moment maps ⓘ pseudoholomorphic curves ⓘ symplectic capacities ⓘ symplectic manifolds ⓘ |
| usesPrerequisite |
Riemannian geometry
ⓘ
algebraic topology ⓘ differential topology ⓘ functional analysis ⓘ |
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: Introduction to Symplectic Topology Description of subject: Introduction to Symplectic Topology is a foundational graduate-level textbook that systematically develops the theory and applications of symplectic manifolds and symplectic geometry.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.