 Teichmüller space

For a fixed closed oriented surface $S_g$, a point is a marked Riemann surface $(X,f:S_g\to X)$, modulo biholomorphisms intertwining the markings up to homotopy. For $g\ge 2$, Fenchel–Nielsen coordinates give real dimension $6g-6$.

Teichmüller space is a fundamental concept in the field of complex analysis and algebraic geometry, specifically in the study of Riemann surfaces. It is named after the mathematician Oswald Teichmüller.