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## manifolds

$$\def\Real{\mathbb{R}} \def\Comp{\mathbb{C}} \def\Rat{\mathbb{Q}} \def\Field{\mathbb{F}} \def\Fun{\mathbf{Fun}} \def\e{\mathbf{e}} \def\f{\mathbf{f}} \def\torus{\mathbb{T}}$$

Manifolds are topological spaces that locally look like Euclidean spaces.

Formalism: charts and atlases. Beware of pathologies (long line; double point…)! Smooth manifolds vs. topological ones.

Inverse function theorem (for a …