Universal Teichmüller space
Encyclopedia
In mathematical complex analysis, universal Teichmüller space T(1) is a Teichmüller space
containing the Teichmüller space T(G) of every Fuchsian group
G. It was introduced by as the set of boundary values of quasiconformal maps of the upper half-plane that fix
0, 1, and ∞.
Teichmüller space
In mathematics, the Teichmüller space TX of a topological surface X, is a space that parameterizes complex structures on X up to the action of homeomorphisms that are isotopic to the identity homeomorphism...
containing the Teichmüller space T(G) of every Fuchsian group
Fuchsian group
In mathematics, a Fuchsian group is a discrete subgroup of PSL. The group PSL can be regarded as a group of isometries of the hyperbolic plane, or conformal transformations of the unit disc, or conformal transformations of the upper half plane, so a Fuchsian group can be regarded as a group acting...
G. It was introduced by as the set of boundary values of quasiconformal maps of the upper half-plane that fix
Fixed point (mathematics)
In mathematics, a fixed point of a function is a point that is mapped to itself by the function. A set of fixed points is sometimes called a fixed set...
0, 1, and ∞.