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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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