smooth manifold

Definition

An $n$-dimensional smooth manifold, $(M, \mathcal{A})$, is an $n$-dimensional topological manifold $M$, equipped with an equivalence class of atlas $\mathcal{A}$, called its smooth structure.

See also

• Riemannian manifold
• Kähler manifold

References

1. https://ncatlab.org/nlab/show/smooth+manifold
2. http://staff.ustc.edu.cn/~wangzuoq/Courses/18F-Manifolds/Notes/Lec02.pdf