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- Gromov's_compactness_theorem_(topology) abstract "For Gromov's compactness theorem in Riemannian geometry, see that article.In the mathematical field of symplectic topology, Gromov's compactness theorem states that a sequence of pseudoholomorphic curves in an almost complex manifold with a uniform energy bound must have a subsequence which limits to a pseudoholomorphic curve which may have nodes or (a finite tree of) "bubbles". A bubble is a holomorphic sphere which has a transverse intersection with the rest of the curve. If the complex structures on the curves in the sequence do not vary, only bubbles may occur (equivalently, the curves that pinch to cause the degeneration of the limiting curve must be contractible). If the complex structures is allowed to vary, nodes can occur as well. Usually, the area bound is achieved by considering a symplectic manifold with compatible almost-complex structure as the target and restricting the images of the curves to lie in a fixed homology class. This theorem underlies the compactness results for flow lines in Floer homology.".
- Gromov's_compactness_theorem_(topology) wikiPageID "6657332".
- Gromov's_compactness_theorem_(topology) wikiPageRevisionID "509348267".
- Gromov's_compactness_theorem_(topology) hasPhotoCollection Gromov's_compactness_theorem_(topology).
- Gromov's_compactness_theorem_(topology) subject Category:Compactness_theorems.
- Gromov's_compactness_theorem_(topology) subject Category:Symplectic_topology.
- Gromov's_compactness_theorem_(topology) type Abstraction100002137.
- Gromov's_compactness_theorem_(topology) type Communication100033020.
- Gromov's_compactness_theorem_(topology) type CompactnessTheorems.
- Gromov's_compactness_theorem_(topology) type Message106598915.
- Gromov's_compactness_theorem_(topology) type Proposition106750804.
- Gromov's_compactness_theorem_(topology) type Statement106722453.
- Gromov's_compactness_theorem_(topology) type Theorem106752293.
- Gromov's_compactness_theorem_(topology) comment "For Gromov's compactness theorem in Riemannian geometry, see that article.In the mathematical field of symplectic topology, Gromov's compactness theorem states that a sequence of pseudoholomorphic curves in an almost complex manifold with a uniform energy bound must have a subsequence which limits to a pseudoholomorphic curve which may have nodes or (a finite tree of) "bubbles". A bubble is a holomorphic sphere which has a transverse intersection with the rest of the curve.".
- Gromov's_compactness_theorem_(topology) label "Gromov's compactness theorem (topology)".
- Gromov's_compactness_theorem_(topology) sameAs m.0ggbdj.
- Gromov's_compactness_theorem_(topology) sameAs Q5610190.
- Gromov's_compactness_theorem_(topology) sameAs Q5610190.
- Gromov's_compactness_theorem_(topology) sameAs Gromov's_compactness_theorem_(topology).
- Gromov's_compactness_theorem_(topology) wasDerivedFrom Gromov's_compactness_theorem_(topology)?oldid=509348267.
- Gromov's_compactness_theorem_(topology) isPrimaryTopicOf Gromov's_compactness_theorem_(topology).