Exterior bundles in diffeology

On diffeological principal bundles of non-formal pseudo-differential operators over formal ones

“…From this first diffeology, one can produce many others, and especially two of them of technical interest, the second one generalizing the nebulae diffeology in a way new to our knowledge: ‚ The 1-dimensional diffeology P 1 (X) made of plots p P P(X) that read locally as p| O = γ ˝f where γ P C 8 (R, X), O is an open subset of an Euclidian space and f P C 8 (O, R). This diffeology is called spaghetti diffeology in [5] and 1-dimensional diffeology in [19]. ‚ The nebulae diffeology, which definition which follows refines the one given independently in [18,19] and [30], and extends the definition of the nebulae diffeology of a manifold.…”

Diffeologies and generalized Kadomtsev-Petviashvili hierarchies

“…The condition that a diffeological vector space is isomorphic with its tangent space at a given point seems natural in a Fréchet setting but becomes not so obvious for a general diffeology. A recent work develops a counter-example in [2].…”