Seminar talk, 11 March 2015
Speaker: Vladimir Medvedev
Title: Basic notions of diffeology
Diffeology is an extension of differential geometry. Using a minimal set of axioms, it allows in a simple but rigorous way to work with objects, which one usually try to avoid in differential geometry: factor-manifolds (not necessarily Hausdorff), spaces of functions, diffeomorphisms groups, spaces of bundles of a fibration and so on. The category of diffeology spaces has many nice properties. For example, it is complete, and cocomplete caetegory, and the category of smooth finite dimensional manifolds with boundary is a full subcategory in it. All main notions of differential geometry (smooth manifold, bundles, tensors, Lie derivatives) carry over to diffeological spaces. I'll explain how to do this.
The talk will require only basic knowledge of differential geometry. It will contain many examples along with all main definitions of diffeology objects.
P.Iglesias-Zemmour, Diffeology, AMS, 2013, available on the net