Variation of Integrals in diffeology
June 9, 2009, update October 21, 2013
 
In this paper we establish first the Stoke theorem for diffeological spaces, then a useful formula in diffeology giving the variation of the integral of a differential p-form on a smooth p-chain in diffeology. With this formula we establish the equivalent for diffeological spaces of the famous Cartan-Lie formula relating Lie derivative, exterior product and contraction of a p-form. We construct also the Chain-Homotopy Operator K from Wp(X) into Wp-1(Paths(X)), which satisfies the property d o K + K o d = 1* - 0*, where 1 and 0 are the maps from Paths(X) to X: 1(g)= g(1)
Canadian Journal of Maths. Use the following reference: Canad. J. Math. Vol. 65 (6), 2013 pp. 1255–1286 
http://dx.doi.org/10.4153/CJM-2012-044-5 
© Canadian Mathematical Society 2012 Any comment or suggestion? Send me a mail...http://dx.doi.org/10.4153/CJM-2012-044-5mailto:piz@math.huji.ac.il?subject=Diffeology%20of%20Manifolds%20with%20Boundaryshapeimage_3_link_0shapeimage_3_link_1
and 0(g)= g(0). Thanks to this operator K we prove the homotopic invariance of the De Rham cohomology for diffeological spaces and in another paper we construct the Moment Map for a closed 2-form defined on a diffeological space.084469EE-D890-4CAA-8A13-1C655A76CF63.htmlshapeimage_4_link_0