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Variations of Integrals in Diffeology
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- Journal:
- Canadian Journal of Mathematics / Volume 65 / Issue 6 / 01 December 2013
- Published online by Cambridge University Press:
- 20 November 2018, pp. 1255-1286
- Print publication:
- 01 December 2013
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- Article
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We establish a 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 Stokes’ 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
$K$, and we apply it here to get the homotopic invariance of De Rham cohomology for diffeological spaces. This is the chain-homotopy operator that is used in symplectic diffeology to construct the moment map.
