Orbifold

Summary

An orbifold is a space that looks near each point like the quotient of an open subset of $\R^n$ by a finite group. It generalizes a smooth manifold, which is the case where all these groups are trivial. Orbifolds arise as quotients of manifolds by properly discontinuous actions of discrete groups, which may have fixed points. They are central in the geometry of surfaces and $3$-manifolds.