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Search: MSC category 58A40 ( Differential spaces )

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1. CJM 2012 (vol 65 pp. 1255)

Iglesias-Zemmour, 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 Cartan-Lie formula. Still in the context of Cartan-De-Rham calculus in diffeology, we construct a Chain-Homotopy Operator $\mathbf K$ 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.

Keywords:diffeology, differential geometry, Cartan-De-Rham calculus
Categories:58A10, 58A12, 58A40

2. CJM 2003 (vol 55 pp. 247)

Cushman, Richard; Śniatycki, Jędrzej
Differential Structure of Orbit Spaces: Erratum
This note signals an error in the above paper by giving a counter-example.

Categories:37J15, 58A40, 58D19, 70H33

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 Stefan-Sussmann 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

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