In this note we give the major steps that show that an open connected oriented four manifold has local holomorphic projective coordinates compatible with a holomorphic foliation obtained by a holomorphic local isomorphism to the complex projective plane minus a point foliated by complex lines through that point. The work of Valentin Poénaru is put in context.

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A Short History of Open Manifolds Related to Complex Analytic Coordinates

  • Dennis Sullivan

摘要

In this note we give the major steps that show that an open connected oriented four manifold has local holomorphic projective coordinates compatible with a holomorphic foliation obtained by a holomorphic local isomorphism to the complex projective plane minus a point foliated by complex lines through that point. The work of Valentin Poénaru is put in context.