Upper half plane
The
upper half plane H is the set of complex numbers
x+
iy such that
y>0. It is the
domain of many functions of interest in
complex analysis, especially
modular forms. It is also a model of the
hyperbolic plane.
There is a group action of SL2(R) on H defined by
-
The action is transitive and the stabilizer of
i is the rotation group
-
Therefore,
H = SL
2(
R)/
K.