Derived smooth manifolds

@article{Spivak2008DerivedSM,
  title={Derived smooth manifolds},
  author={David I. Spivak},
  journal={Duke Mathematical Journal},
  year={2008},
  volume={153},
  pages={55-128}
}
  • David I. Spivak
  • Published 29 October 2008
  • Mathematics
  • Duke Mathematical Journal
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… 
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