Resumen:
The space of hyperbolic metrics on a (marked) hyperbolic surface was
studied by Teichmueller around 1940. An alternative viewpoint is via
discrete and faithful representations to SL(2,R) of the fundamental
group. Later the space of discrete and faithful (quasi-Fuchsian)
representations of a surface group to SL(2,C) were considered. More
recently, the space of representations to SU(2,1) has been a subject
of much research. I will briefly outline the two classical sitautions
and then give a survey of known work in the case of SU(2,1).
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