Derived Smooth Manifolds

Understand

We define a simplicial category called the category of derived manifolds.

• It contains the category of smooth manifolds as a full discrete subcategory, and it is closed under taking arbitrary intersections in a manifold.
• A derived manifold is a space together with a sheaf of local $C^\infty$-rings that is obtained by patching together homotopy zero-sets of smooth functions on Euclidean spaces.
• We show that derived manifolds come equipped with a stable normal bundle and can be imbedded into Euclidean space.