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Variations of Integrals in Diffeology

  Published:2012-12-29
 Printed: Dec 2013
  • Patrick Iglesias-Zemmour,
    LATP-CNRS, 39 rue F. Joliot-Curie, 13453 Marseille Cedex 13, France
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Abstract

We establish the formula for the variation of integrals of differential forms on cubic chains, in the context of diffeological spaces. Then, we establish the diffeological version of Stoke's theorem, and we apply that to get the diffeological variant of the Cartan-Lie formula. Still in the context of Cartan-De-Rham calculus in diffeology, we construct a Chain-Homotopy Operator $\mathbf K$ we apply it here to get the homotopic invariance of De Rham cohomology for diffeological spaces. This is the Chain-Homotopy Operator which used in symplectic diffeology to construct the Moment Map.
Keywords: diffeology, differential geometry, Cartan-De-Rham calculus diffeology, differential geometry, Cartan-De-Rham calculus
MSC Classifications: 58A10, 58A12, 58A40 show english descriptions Differential forms
de Rham theory [See also 14Fxx]
Differential spaces
58A10 - Differential forms
58A12 - de Rham theory [See also 14Fxx]
58A40 - Differential spaces
 

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