Teichmüller space

In mathematics, the Teichmüller space T_X of a (real) 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. Each point in T_X may be regarded as an isomorphism class of 'marked' Riemann surfaces where a 'marking' is an isotopy class of homeomorphisms from X to X.