250096 VO Analysis on Manifolds (2024S)

This course is in the core modules for the area "geometry and topology" of the master program and provides the basis for large parts of this area. It discusses the basic theory of (abstract) smooth manifolds and analysis thereon, which is the foundation of differential geometry. We will discuss the fundamental geometric objects (vector fields, tensor fields, differential forms) available on smooth manifolds and the basic operations dealing with such objects. We will also deal with integration on manifolds and Stokes theorem in the setting of manifolds with boundary. On the way we will discuss several applications of the techniques in areas between analysis and geometry, for example to Riemannian and symplectic geometry.