广义微分几何讲义 Lectures On Diffeology

"Diffeology¿¿¿¿¿¿¿¿¿¿¿¿Lectures written by leading figures in diffeology research¿¿¿¿Brief Introduction¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿Diffeology¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿Diffeology¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿These lecture notes are intended for students interested in differential geometry, particularly in situations not covered by the classical theory. The first part is a series of lectures given at Shantou University as a special program. They introduce the main areas of differential geometry extended to diffeology, as developed in the chapters of the diffeology textbook. The second part consists of a series of notes and exercises chosen because they do not fall within the scope of the theory of manifolds. They illustrate some applications of diffeology: infinite spaces with singular quotients, symplectic diffeological space without Hamiltonian diffeomorphisms, general spaces of geodesics, Riemannian diffeology program, classifying space of quasi-spheres, and other examples. They have been chosen to familiarise the student with some specific techniques used in the versatile environment of diffeology. ¿¿¿¿Author Introdcution¿¿¿¿·¿¿¿¿¿¿-¿¿¿¿Patrick Iglesias-Zemmour¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿Diffeology¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿Patrick Iglesias-Zemmour is a researcher at the French National Center for Scientific Research (CNRS) and a long-term visiting professor at The Hebrew University of Jerusalem. He is renowned for his work in symplectic geometry and diffeology. His book ¿Diffeology¿ stands as the first international textbook in this field. ¿Lectures On Diffeology¿ offers a fresh presentation of his years of research achievements, complementing and echoing the content of ¿Diffeology¿.