Kleinian model explained
where
is a
discrete subgroup of PSL(2,
C). Here, the subgroup
, a
Kleinian group, is defined so that it is isomorphic to the
fundamental group
of the surface
N. Many authors use the terms
Kleinian group and
Kleinian model interchangeably, letting one stand for the other. The concept is named after
Felix Klein.
Many properties of Kleinian models are in direct analogy to those of Fuchsian models; however, overall, the theory is less well developed. A number of unsolved conjectures on Kleinian models are the analogs to theorems on Fuchsian models.
See also