turkmath.org

A 12 hours course by Patrick Iglesias-Zemmour, in the framework of the Program on Diffeology Studies, managed by Serap Gürer, sponsored by Tubitak-Galatasaray for the years 2016-17-18, and supported by the Consortium. This course will introduce the following subjects with examples and exercises. 1. Diffeological Spaces, Smooth Maps, the Category {Diffeology}, Fineness etc. 2. Operations on Diffeologies: Products, Sums, Parts, Quotients. 3. Functional Diffeology. 4. Local Smooth Maps, D-Topology. 5. Homotopy: Definition of Higher Homotopy Groups, Relative Homotopy Long Sequence. 6. Differential calculus: Definition of Differential Forms, De Rham Cohomology, Chain-Homotopy Operator, Homotopic Invariance of De Rham Cohomology. 7. Fiber Bundles: Definition, Long Exact Sequence in Homotopy, Homotopic Equivalence of Pullbacks, Connections etc.

Serap Gürer: sgurer@gsu.edu.tr