On Derham Theorem in Synthetic Differential Geometry

Félix, Yves;Lavendhomme, René
(1990) Journal of Pure and Applied Algebra — Vol. 69, n° 1, p. 21-31 (1990)

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  • Félix, YvesUCLouvain
    Author
  • Lavendhomme, RenéUCLouvain
    Author
Abstract
In classical differential geometry the integration morphism intergal: omega-(p)(M) --> S(p)(M) is a morphism of complexes inducing an isomorphism in homology. In the synthetic case the two complexes are in fact isomorphic. We exhibit a cochain morphism D: S(p)(M) --> omega-(p)(M), which is an inverse for integral.
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Félix, Y., & Lavendhomme, R. (1990). On Derham Theorem in Synthetic Differential Geometry. Journal of Pure and Applied Algebra, 69(1), 21-31. https://doi.org/10.1016/0022-4049(90)90075-S (Original work published 1990)