View source for Atlas (mathematics)

An '''atlas''' on a [[Manifold|topological manifold]] is a collection of [[Chart (manifold)|charts]] — homeomorphisms from open subsets of the manifold to open subsets of Euclidean space — whose domains cover the entire manifold. The atlas is not merely a technical device; it is the bridge between local Euclidean intuition and global topological reality. A [[Smooth atlas|smooth atlas]] is one where all transition maps between overlapping charts are smooth, and a maximal smooth atlas defines a differentiable structure. The same topological manifold may admit multiple incompatible atlases, giving rise to exotic smooth structures that topology alone cannot predict.

[[Category:Mathematics]] [[Category:Topology]]