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Teichmüller space
Parametrizes complex structures on a surface
Teichmüller space
In mathematics, the Teichmüller space T ( S ) {\displaystyle T(S)} of a (real) topological (or differential) surface S {\displaystyle S} is a space that parametrizes complex structures on S {\displaystyle S} up to the action of homeomorphisms that are isotopic to the identity homeomorphism. Teichmüller spaces are named after Oswald Teichmüller. Each point in a Teichmüller space T ( S ) {\displaystyle T(S)} may be regarded as an isomorphism class of "marked" Riemann surfaces, where a "marking" is an isotopy class of homeomorphisms from S {\displaystyle S} to itself. It can be viewed as a moduli space for marked hyperbolic structure on the surface, and this endows it with a natural topology for which it is homeomorphic to a ball...
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