Special Interest Group

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Defining Riemann surfaces

Soumis par Mika.Seppala le lun, 2008/02/11 - 23:04.

Excluding certain special cases, a Riemann surface $ X $ has the unit disk $ D $ as its universal cover. Hence

\[X=D/G\]

where $ G $ is a group of Möbius transformations. If $ X $ is compact, $ G $ is finitely generated.

When defining Riemann surfaces for computations one may simply give the generators of the group $ G $ (and the relations that the generator satisfy).

Now the problem is:

  • How to find Möbius transformations which generate a discontinuous group?
  • How to perform the Fenchel Nielsen twists and other deformations of such group?