Uniformization Theorem - Complex Classification

Complex Classification

Every Riemann surface is the quotient of a free, proper and holomorphic action of a discrete group on its universal covering and this universal covering is holomorphically isomorphic (one also says: "conformally equivalent") to one of the following:

  1. the Riemann sphere
  2. the complex plane
  3. the unit disk in the complex plane.

Read more about this topic:  Uniformization Theorem

Famous quotes containing the word complex:

    “When distant and unfamiliar and complex things are communicated to great masses of people, the truth suffers a considerable and often a radical distortion. The complex is made over into the simple, the hypothetical into the dogmatic, and the relative into an absolute.”
    —Walter Lippmann (1889–1974)