differentiable manifold

Another word for a C^∞ (infinitely differentiable) manifold, also called a differentiable manifold. A smooth manifold is a topological manifold together with its "functional structure" and so differs from a topological manifold because the notion of differentiability exists on it. Every smooth manifold is a topological manifold, but not necessarily vice versa. (The first nonsmooth topological manifold occurs in four dimensions.) Milnor showed that a seven-dimensional hypersphere can be made into a smooth manifold in 28 ways.

exotic R^4 | exotic sphere | hypersphere | manifold | smooth structure | topological manifold