1. CJM 2012 (vol 65 pp. 1255)
 IglesiasZemmour, Patrick

Variations of Integrals in Diffeology
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
CartanLie formula. Still in the context of CartanDeRham calculus
in diffeology, we
construct a ChainHomotopy Operator $\mathbf K$ we apply it here to
get the homotopic invariance of De Rham cohomology for
diffeological spaces. This is the ChainHomotopy Operator which used in
symplectic diffeology to construct the Moment Map.
Keywords:diffeology, differential geometry, CartanDeRham calculus Categories:58A10, 58A12, 58A40 

2. CJM 2003 (vol 55 pp. 247)
3. CJM 2001 (vol 53 pp. 715)
 Cushman, Richard; Śniatycki, Jędrzej

Differential Structure of Orbit Spaces
We present a new approach to singular reduction of Hamiltonian systems
with symmetries. The tools we use are the category of differential
spaces of Sikorski and the StefanSussmann theorem. The former is
applied to analyze the differential structure of the spaces involved
and the latter is used to prove that some of these spaces are smooth
manifolds.
Our main result is the identification of accessible sets of the
generalized distribution spanned by the Hamiltonian vector fields of
invariant functions with singular reduced spaces. We are also able
to describe the differential structure of a singular reduced space
corresponding to a coadjoint orbit which need not be locally closed.
Keywords:accessible sets, differential space, Poisson algebra, proper action, singular reduction, symplectic manifolds Categories:37J15, 58A40, 58D19, 70H33 
