Variation of Integrals in diffeology
June 9, 2009, update September 2, 2012
 
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)
To be published in the Canadian Journal of Maths. For comment or suggestion, just send me a mail...mailto:piz@math.huji.ac.il?subject=Diffeology%20of%20Manifolds%20with%20Boundaryshapeimage_3_link_0
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