Gromov-Witten invariant

In mathematics, specifically in symplectic topology and algebraic geometry, Gromov-Witten (GW) invariants are rational numbers that count pseudoholomorphic curves meeting prescribed conditions in a given symplectic manifold. The GW invariants may be packaged as a homology or cohomology class in an appropriate space, or as the deformed cup product of quantum cohomology. These invariants have been used to distinguish symplectic manifolds; they also play a crucial role in type IIA string theory.

Related Topics:
Mathematics - Symplectic topology - Algebraic geometry - Rational number - Pseudoholomorphic curve - Symplectic manifold - Homology - Cohomology - Type IIA - String theory

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The rigorous mathematical definition of Gromov-Witten invariants is lengthy and difficult, so it is treated separately in the stable map article. This article attempts a more intuitive explanation of what the invariants mean, how they are computed, and why they are important.

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