Study of geometric properties preserved under continuous deformations.
A manifold is a space that, near each point, looks like regular flat space (like a line or a plane), but can be curved or twisted on a larger scale.
Manifolds can exist in any number of dimensions—even ones we can't visualize!
Manifolds are the playground for much of modern mathematics and physics, from black holes in general relativity to the shapes of molecules.
The surface of the Earth is a 2D manifold (a sphere).
The path traced by a gymnast's ribbon in space forms a 1D manifold.
Manifolds are spaces that look locally flat but can have amazing global shapes.