”Teichmuller space” 良く纏まっている
https://en.wikipedia.org/wiki/Teichm%C3%BCller_space
Teichmuller space

The geometric vein in the study of Teichmuller space was revived following the work of William Thurston in the late seventies, who introduced a geometric compactification which he used in his study of the mapping class group of a surface.
Other more combinatorial objects associated to this group (in particular the curve complex) have also been related to Teichmuller space, and this is a very active subject of research in geometric group theory.

Quadratic differentials and the Bers embedding
Main article: Schwarzian derivative
Main article: Bers slice

https://upload.wikimedia.org/wikipedia/commons/thumb/7/71/Bers-Einbettung.png/220px-Bers-Einbettung.png
Image of the Bers embedding of a punctured torus' 2-dimensional Teichmuller space

https://en.wikipedia.org/wiki/Moduli_of_algebraic_curves
Moduli of algebraic curves

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