Fuchsian group [SEP] named after
" of hyperbolic geometry).
General Fuchsian groups were first studied by , who was motivated by the paper , and therefore named them after Lazarus Fuchs.
Fuchsian groups on the upper half-plane.
Let H = {"z" in C : Im("z")  0} be the upper half-plane. Then H is a model of the hyperbolic plane when endowed with the metric
The group PSL(2,R) acts on H by linear fractional transformations (also known as Möbius transformations):
This
Bers slice
In the mathematical theory of Kleinian groups, Bers slices and Maskit slices, named after Lipman Bers and Bernard Maskit, are certain slices through the moduli space of Kleinian groups.
Bers slices.
For a quasi-Fuchsian group. the limit set is a Jordan curve whose complement has two components. The quotient of each of these components by the groups is a Riemann surface, so we get a map from marked quasi-Fuchsian groups to pairs of Riemann surfaces, and hence to a product of two