Differential Geometry (Mastermath course, Fall 2013)
Location and time:
There will be hand-in problems. They will count for 50 percent of your
grade. At the end of the course there will be a take home exam.
So far these were the homework problems:
And this was the final exam.
Please do all the exercises in the lecture notes. The hand-in problems will be posted on this page, as a separate sheet
Lecture notes: Lecture notes might be made available during the course, but only when the lecturer's treatment of the subject substantially differs from the treatment in the literature.
The schedule week by week (here we will try to add, after each lecture, a description of what was discussed in the
lectures + the exercises):
Aim/content of the course:
The aim of this course is to provide an introduction to the general concept of a G-structure, which includes several significant geometric structures on differentiable manifolds (for instance, Riemannian or symplectic structures).
The course will start with a discussion of "geometric structures" on vector spaces and on manifolds.
Some of the key-words are: Riemannian metrics, distributions, foliations, symplectic structures, almost complex and complex structures.
We will then introduce the concept of a G-structure on a manifold and concentrate on the general framework that allows us to take this more general (abstract) point of view: Lie groups and Lie algebras, principal bundles, and connections.
The last part of the course will focus on topics such as equivalence and integrability of G-structures and discuss their interpretation in the some specific examples.
We will occasionally use lecture notes (see above).
The main reference for this course is:
Last update: 30-1-2014