## Vector fields and differential forms on a near-point manifold. (Champs de vecteurs et formes différentielles sur une variété des points proches.)(French)Zbl 1212.13016

Summary: Let $$M$$ be a smooth manifold, $$A$$ be a local algebra in the sense of André Weil, $$M^{A}$$ be the manifold of near points on $$M$$ of kind $$A$$ and $$\mathfrak {X}(M^{A})$$ be the module of vector fields on $$M^{A}$$. We give a new definition of vector fields on $$M^{A}$$ and we show that $$\mathfrak {X}(M^{A})$$ is a Lie algebra over $$A$$. We study the cohomology of $$A$$-differential forms.

### MSC:

 13H99 Local rings and semilocal rings 58A05 Differentiable manifolds, foundations 58A10 Differential forms in global analysis
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