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- Quantum_cohomology abstract "In mathematics, specifically in symplectic topology and algebraic geometry, a quantum cohomology ring is an extension of the ordinary cohomology ring of a closed symplectic manifold. It comes in two versions, called small and big; in general, the latter is more complicated and contains more information than the former. In each, the choice of coefficient ring (typically a Novikov ring, described below) significantly affects its structure, as well.While the cup product of ordinary cohomology describes how submanifolds of the manifold intersect each other, the quantum cup product of quantum cohomology describes how subspaces intersect in a \"fuzzy\", \"quantum\" way. More precisely, they intersect if they are connected via one or more pseudoholomorphic curves. Gromov–Witten invariants, which count these curves, appear as coefficients in expansions of the quantum cup product.Because it expresses a structure or pattern for Gromov–Witten invariants, quantum cohomology has important implications for enumerative geometry. It also connects to many ideas in mathematical physics and mirror symmetry. In particular, it is ring-isomorphic to symplectic Floer homology.Throughout this article, X is a closed symplectic manifold with symplectic form ω.".
- Quantum_cohomology wikiPageID "7781359".
- Quantum_cohomology wikiPageLength "9950".
- Quantum_cohomology wikiPageOutDegree "45".
- Quantum_cohomology wikiPageRevisionID "698256151".
- Quantum_cohomology wikiPageWikiLink Algebraic_geometry.
- Quantum_cohomology wikiPageWikiLink Almost_complex_manifold.
- Quantum_cohomology wikiPageWikiLink Associative_property.
- Quantum_cohomology wikiPageWikiLink Category:Algebraic_geometry.
- Quantum_cohomology wikiPageWikiLink Category:Cohomology_theories.
- Quantum_cohomology wikiPageWikiLink Category:String_theory.
- Quantum_cohomology wikiPageWikiLink Category:Symplectic_topology.
- Quantum_cohomology wikiPageWikiLink Chern_class.
- Quantum_cohomology wikiPageWikiLink Closed_manifold.
- Quantum_cohomology wikiPageWikiLink Cohomology_ring.
- Quantum_cohomology wikiPageWikiLink Complex_number.
- Quantum_cohomology wikiPageWikiLink Connection_(mathematics).
- Quantum_cohomology wikiPageWikiLink Cup_product.
- Quantum_cohomology wikiPageWikiLink Curvature.
- Quantum_cohomology wikiPageWikiLink Differential_equation.
- Quantum_cohomology wikiPageWikiLink Distributive_property.
- Quantum_cohomology wikiPageWikiLink Enumerative_geometry.
- Quantum_cohomology wikiPageWikiLink Floer_homology.
- Quantum_cohomology wikiPageWikiLink Frobenius_algebra.
- Quantum_cohomology wikiPageWikiLink Frobenius_manifold.
- Quantum_cohomology wikiPageWikiLink Fubini–Study_metric.
- Quantum_cohomology wikiPageWikiLink Generating_function.
- Quantum_cohomology wikiPageWikiLink Gromov–Witten_invariant.
- Quantum_cohomology wikiPageWikiLink Homology_(mathematics).
- Quantum_cohomology wikiPageWikiLink Ideal_(ring_theory).
- Quantum_cohomology wikiPageWikiLink Identity_element.
- Quantum_cohomology wikiPageWikiLink Intersection_theory.
- Quantum_cohomology wikiPageWikiLink Isomorphism.
- Quantum_cohomology wikiPageWikiLink Kronecker_delta.
- Quantum_cohomology wikiPageWikiLink Mathematical_physics.
- Quantum_cohomology wikiPageWikiLink Mathematics.
- Quantum_cohomology wikiPageWikiLink Mirror_symmetry_(string_theory).
- Quantum_cohomology wikiPageWikiLink Poincaré_duality.
- Quantum_cohomology wikiPageWikiLink Potential.
- Quantum_cohomology wikiPageWikiLink Power_series.
- Quantum_cohomology wikiPageWikiLink Projective_plane.
- Quantum_cohomology wikiPageWikiLink Pseudoholomorphic_curve.
- Quantum_cohomology wikiPageWikiLink Ring_(mathematics).
- Quantum_cohomology wikiPageWikiLink Symplectic_geometry.
- Quantum_cohomology wikiPageWikiLink Symplectic_manifold.
- Quantum_cohomology wikiPageWikiLink Tangent_bundle.
- Quantum_cohomology wikiPageWikiLink Torsion_subgroup.
- Quantum_cohomology wikiPageWikiLink Torsion_tensor.
- Quantum_cohomology wikiPageWikiLink Vector_bundle.
- Quantum_cohomology wikiPageWikiLink WDVV_equation.
- Quantum_cohomology wikiPageWikiLinkText "(small) quantum cohomology".
- Quantum_cohomology wikiPageWikiLinkText "Novikov ring".
- Quantum_cohomology wikiPageWikiLinkText "Quantum cohomology".
- Quantum_cohomology wikiPageWikiLinkText "quantum cohomology".
- Quantum_cohomology wikiPageUsesTemplate Template:Cite_arXiv.
- Quantum_cohomology wikiPageUsesTemplate Template:See_also.
- Quantum_cohomology subject Category:Algebraic_geometry.
- Quantum_cohomology subject Category:Cohomology_theories.
- Quantum_cohomology subject Category:String_theory.
- Quantum_cohomology subject Category:Symplectic_topology.
- Quantum_cohomology hypernym Extension.
- Quantum_cohomology type Software.
- Quantum_cohomology type Physic.
- Quantum_cohomology type Theory.
- Quantum_cohomology type Thing.
- Quantum_cohomology comment "In mathematics, specifically in symplectic topology and algebraic geometry, a quantum cohomology ring is an extension of the ordinary cohomology ring of a closed symplectic manifold. It comes in two versions, called small and big; in general, the latter is more complicated and contains more information than the former.".
- Quantum_cohomology label "Quantum cohomology".
- Quantum_cohomology seeAlso Novikov_ring.
- Quantum_cohomology sameAs Q7269022.
- Quantum_cohomology sameAs 量子コホモロジー.
- Quantum_cohomology sameAs 양자_코호몰로지.
- Quantum_cohomology sameAs m.026cw73.
- Quantum_cohomology sameAs Q7269022.
- Quantum_cohomology wasDerivedFrom Quantum_cohomology?oldid=698256151.
- Quantum_cohomology isPrimaryTopicOf Quantum_cohomology.