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arXiv · 2212.11163

Differential forms on $C^\infty$-ringed spaces

Eugene Lerman
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Abstract

We construct a complex of differential forms on a local $C^\infty$-ringed space. The two main classes of spaces we have in mind are differential spaces in the sense of Sikorski and $C^\infty$-schemes. Just as in the case of manifolds the construction is functorial. Consequently forms can be integrated over simplices and Stokes' theorem holds.

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Eugene Lerman. 2022-12-21. Differential forms on $C^\infty$-ringed spaces. https://doi.org/10.1016/j.geomphys.2023.105062

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