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- Trivial_cylinder abstract "In geometry and topology, trivial cylinders are certain pseudoholomorphic curves appearing in certain cylindrical manifolds.In Floer homology and its variants, chain complexes or differential graded algebras are generated by certain combinations of closed orbits of vector fields. In symplectic Floer homology, one considers the Hamiltonian vector field of a Hamiltonian function on a symplectic manifold; in symplectic field theory, contact homology, and their variants, one considers the Reeb vector field associated to a contact form, or more generally a stable Hamiltonian structure.The differentials all count some flavor of pseudoholomorphic curves in a manifold with a cylindrical almost-complex structure whose ends at negative infinity are the given collection of closed orbits. For instance, in symplectic Floer homology, one considers the product of the mapping torus of a symplectomorphism with the real numbers; in symplectic field theory, one considers the symplectization of a contact manifold.The product of a given embedded closed orbit with R is always a pseudoholomorphic curve, and such a curve is called a trivial cylinder. Trivial cylinders do not generally contribute to the aforementioned differentials, but they may appear as components of more complicated curves which do.".
- Trivial_cylinder wikiPageID "25523411".
- Trivial_cylinder wikiPageRevisionID "337411914".
- Trivial_cylinder hasPhotoCollection Trivial_cylinder.
- Trivial_cylinder subject Category:Algebraic_geometry.
- Trivial_cylinder subject Category:Complex_manifolds.
- Trivial_cylinder subject Category:Symplectic_topology.
- Trivial_cylinder type Artifact100021939.
- Trivial_cylinder type ComplexManifolds.
- Trivial_cylinder type Conduit103089014.
- Trivial_cylinder type Manifold103717750.
- Trivial_cylinder type Object100002684.
- Trivial_cylinder type Passage103895293.
- Trivial_cylinder type PhysicalEntity100001930.
- Trivial_cylinder type Pipe103944672.
- Trivial_cylinder type Tube104493505.
- Trivial_cylinder type Way104564698.
- Trivial_cylinder type Whole100003553.
- Trivial_cylinder type YagoGeoEntity.
- Trivial_cylinder type YagoPermanentlyLocatedEntity.
- Trivial_cylinder comment "In geometry and topology, trivial cylinders are certain pseudoholomorphic curves appearing in certain cylindrical manifolds.In Floer homology and its variants, chain complexes or differential graded algebras are generated by certain combinations of closed orbits of vector fields.".
- Trivial_cylinder label "Trivial cylinder".
- Trivial_cylinder sameAs m.09rwf1j.
- Trivial_cylinder sameAs Q7844659.
- Trivial_cylinder sameAs Q7844659.
- Trivial_cylinder sameAs Trivial_cylinder.
- Trivial_cylinder wasDerivedFrom Trivial_cylinder?oldid=337411914.
- Trivial_cylinder isPrimaryTopicOf Trivial_cylinder.