1
$\begingroup$

It is known that (uniformization theorem) any Riemann surface can be written as the quotient of its universal cover by a discrete group (of Möbius transformations). This group is isomorphic to the fundamental group of the surface. My question is:

Can we choose a non-discrete group that is isomorphic to the fundamental group of the surface? What happens if we consider the quotient? (I know that it is not a surface in general).

In other words:

What happens if we quotient the upper-half plane by a non-discrete group?

Is it interesting to study such quotients? If so, why?

  • 0
    @yaa09d: Well, I'm certainly not prepared to answer "no" to such a broad question...but nothing positive comes to mind.2012-02-29

0 Answers 0