%0 Journal Article
%T Variations of integrals in diffeology
%+ Laboratoire d'Analyse, Topologie, Probabilités (LATP)
%A Iglesias-Zemmour, Patrick
%< avec comité de lecture
%@ 0008-414X
%J Canadian Journal of Mathematics
%I University of Toronto Press
%V 65
%N 6
%P 1255-1286
%8 2013
%D 2013
%R 10.4153/CJM-2012-044-5
%K diffeology
%K differential geometry
%K Cartan-De-Rham calculus
%Z 58A10, 58A12, 58A40
%Z Mathematics [math]/Differential Geometry [math.DG]
%Z Mathematics [math]/Symplectic Geometry [math.SG]Journal articles
%X 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 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.
%G English
%L hal-01288538
%U https://hal.science/hal-01288538
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ INSMI