McDuff–Salamon theory of J-holomorphic curves

E621122

framework for pseudoholomorphic curves mathematical theory theory in symplectic geometry

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.

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Observed surface forms (1)

Surface form	Occurrences
J-holomorphic Curves and Symplectic Topology	1

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 ⓘ

Referenced by (2)

Full triples — surface form annotated when it differs from this entity's canonical label.

Dusa McDuff → notableWork → McDuff–Salamon theory of J-holomorphic curves ⓘ

Dusa McDuff → authorOf → McDuff–Salamon theory of J-holomorphic curves ⓘ

this entity surface form: J-holomorphic Curves and Symplectic Topology