Get Math Help

GET TUTORING NEAR ME!

(800) 434-2582

By submitting the following form, you agree to Club Z!'s Terms of Use and Privacy Policy

    Home / Get Math Help

    Smooth Structure

    Definition

    A smooth structure on a topological manifold (also called a differentiable structure) is given by a smooth atlas of coordinate charts, i.e., the transition functions between the coordinate charts are C^∞ smooth. A manifold with a smooth structure is called a smooth manifold (or differentiable manifold). A smooth structure is used to define differentiability for real-valued functions on a manifold. This extends to a notion of when a map between two differentiable manifolds is smooth, and naturally to the definition of a diffeomorphism. In addition, the smooth structure is used to define manifold tangent vectors, the collection of which is the tangent bundle.

    Back to List | POWERED BY THE WOLFRAM LANGUAGE