The upper half plane and its automorphisms #
This file defines
upper_half_plane to be the upper half plane in
We furthermore equip it with the structure of an
SL(2,ℝ) action by
fractional linear transformations.
We define the notation
ℍ for the upper half plane available in the locale
upper_half_plane so as not to conflict with the quaternions.
The open upper half plane
The action of
SL(2, ℝ) on the upper half-plane by fractional linear transformations.