An Introduction to Diffeology

@inproceedings{IGLESIASZEMMOUR2021AnIT,
  title={An Introduction to Diffeology},
  author={Patrick IGLESIAS-ZEMMOUR},
  year={2021}
}
This text presents the basics of Diffeology and themain domains: Homotopy, FiberBundles,Quotients, Singularities, Cartan-deRhamCalculus —which form the core of differential geometry— from the point of view of this theory. We show what makes diffeology special and relevant in regard to these traditional subjects. 
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References

SHOWING 1-10 OF 80 REFERENCES
A model structure on the category of diffeological spaces
We construct a model category structure on the category of diffeological spaces which is Quillen equivalent to the model structure on the category of topological spaces based on the notions of Serre
Example of singular reduction in symplectic diffeology
We present an example of symplectic reduction in diffeology where the space involved is infinite dimensional and the reduction is singular. This example is a mix of two cases that are not handled by
Homology and cohomology via enriched bifunctors
We show that the category of numerically generated pointed spaces is complete, cocomplete, and monoidally closed with respect to the smash product, and then utilize these features to establish a
Homotopy structures of smooth CW complexes
In this paper we present the notion of smooth CW complexes given by attaching cubes on the category of diffeological spaces, and we study their smooth homotopy structures related to the homotopy
Moment maps and diffeomorphisms
Atiyah and Bott pointed out, in [1], that the curvature of a connection on a bundle over a surface can be viewed as the “momentum” corresponding to the action of the gauge group. This observation,
Simple non-rational convex polytopes via symplectic geometry
ON A GENERALIZATION OF THE NOTION OF MANIFOLD BY
where H is the product of the lengths of all the hooks in [X]. This formula is of general interest, since it gives a simple interpretation for the quotient n!/fX. Note that expression (2.2) is the
The Convenient Setting of Global Analysis
Introduction Calculus of smooth mappings Calculus of holomorphic and real analytic mappings Partitions of unity Smoothly realcompact spaces Extensions and liftings of mappings Infinite dimensional
...
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