Curves | Symplectic topology | Algebraic geometry | Complex manifolds

Pseudoholomorphic curve

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. (Wikipedia).

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Pseudosphere

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From playlist Short Talks by Postdoctoral Members

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Holomorphic curve | Path integral formulation | String theory | Topology | Almost complex manifold | Hamiltonian vector field | Non-squeezing theorem | Gromov's compactness theorem (topology) | Stable map | Euler characteristic | Closed manifold | Gromov–Witten invariant | Riemann surface | Mathematics | Cauchy–Riemann equations | Floer homology | Compact space | Algebraic curve | Complex number | Moduli space | Symplectic manifold | Geometry