Special Interest Group

Defining Riemann surfaces

Enviado por Mika.Seppala el 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?

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