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

Eugene Lerman

doi:10.1016/j.geomphys.2023.105062

paper

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

arXiv:2212.11163 · doi:10.1016/j.geomphys.2023.105062

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.

v3: 38 pages. Paper shortened by removal of expository material

Differential forms on C∞-ringed spaces

Abstract

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