Seminar talk, 11 March 2015

Speaker: Vladimir Medvedev

Title: Basic notions of diffeology

Abstract:
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.

References:
P.Iglesias-Zemmour, Diffeology, AMS, 2013, available on the net

M.Vincent, Diffeological differential geometry, Master thesis, Univ. Copenhagen, 2008, local copy

Y.Karshon, An Invitation to Diffeology, talk at Conf. Poisson 2014, video on youtube, local copy