Pseudo holomorphic curves in symplectic manifolds

  title={Pseudo holomorphic curves in symplectic manifolds},
  author={Mikhael Gromov},
  journal={Inventiones mathematicae},
  • M. Gromov
  • Published 1985
  • Mathematics
  • Inventiones mathematicae
Definitions. A parametrized (pseudo holomorphic) J-curve in an almost complex manifold (IS, J) is a holomorphic map of a Riemann surface into Is, say f : (S, J3 ~(V, J). The image C=f(S)C V is called a (non-parametrized) J-curve in V. A curve C C V is called closed if it can be (holomorphically !) parametrized by a closed surface S. We call C regular if there is a parametrization f : S ~ V which is a smooth proper embedding. A curve is called rational if one can choose S diffeomorphic to the… Expand
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