250096 VO Analysis on manifolds (2020S)

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 basic 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. In the end of the course, we will discuss several applications of the techniques in areas between analysis and geometry, for example basics of symplectic and contact geometry.

For the period of home learning, students are expected to study the material following the lecture notes. The moodle page for the course containes detailes information on the material that should be studied, additional texts on parts of the lecture notes and a forum, in which students can pose questions and initiate discussions.