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High Quality Content by WIKIPEDIA articles! In mathematics, specifically in topology and geometry, a pseudoholomorphic curve (or J-holomorphic curve) is a smooth map from a Riemann surface into an almost complex manifold that satisfies the Cauchy-Riemann equation. Introduced in 1985 by Mikhail Gromov, pseudoholomorphic curves have since revolutionized the study of symplectic manifolds. In particular, they lead to the Gromov-Witten invariants and Floer homology, and play a prominent role in string theory.