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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 subspaces 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 Floer homology.Throughout this article, X is a closed symplectic manifold with symplectic form ω.".
- Quantum_cohomology wikiPageID "7781359".
- Quantum_cohomology wikiPageRevisionID "599464752".
- Quantum_cohomology hasPhotoCollection Quantum_cohomology.
- 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 type Abstraction100002137.
- Quantum_cohomology type Cognition100023271.
- Quantum_cohomology type CohomologyTheories.
- Quantum_cohomology type Explanation105793000.
- Quantum_cohomology type HigherCognitiveProcess105770664.
- Quantum_cohomology type Process105701363.
- Quantum_cohomology type PsychologicalFeature100023100.
- Quantum_cohomology type Theory105989479.
- Quantum_cohomology type Thinking105770926.
- 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 label "量子コホモロジー".
- Quantum_cohomology sameAs 量子コホモロジー.
- Quantum_cohomology sameAs m.026cw73.
- Quantum_cohomology sameAs Q7269022.
- Quantum_cohomology sameAs Q7269022.
- Quantum_cohomology sameAs Quantum_cohomology.
- Quantum_cohomology wasDerivedFrom Quantum_cohomology?oldid=599464752.
- Quantum_cohomology isPrimaryTopicOf Quantum_cohomology.