Geometry 2

The aim of this course is to introduce some basic concpets from differential geometry, including Lie groups and principal fibrations, which are essential in some parts of theoretical physics. In the last part of the course we introduce De Rham cohomology and complex manifolds.

At the end of the course, the student will have acquired the following skills:

1) knows how to use the concepts and methods of differential geometry
2) will be able to understand and use vector fields and differential forms
3) will be able to understand and use properties of Lie groups (left invariant vector fields, the Lie algebra and the canonical one form)
4) will be able to understand principal fibrations and connections
5) will be able to understand and use De Rham cohomology (Poincare' Lemma, the Mayer-Vietoris sequence, cohomology groups of spheres and projective spaces)