Teichmüller space

Teichmüller space is a mathematical concept that describes all the different ways a given shape, called a surface (like a doughnut-shaped torus), can be stretched, deformed, and reshaped without tearing or gluing. Each point in this space represents a unique version of that surface’s geometric structure, capturing its possible conformal (angle-preserving) forms. Essentially, it provides a way to study the variety of complex structures a surface can have, helping mathematicians understand how surfaces behave under deformation while preserving their essential features.