The idea of the course is to provide notions of topology and geometry to mathematical physicists, as well as present concrete applications of such notions to pure algebraists and geometers.
The idea would be not to fall in a too abstract presentation, and to anchor it into examples taken from physics. I propose to start from the basics and grow in complexity to reach higher grounds which are much more intricate. Here is a tentative plan of what i would like to talk about. I think most items need more than one seance and maybe not everything could be addressed.