Complex-symbolic seminar, October 27

 Matthias Wagner (EPF, Lausanne):
 

On the classification of flat Riemannian manifolds

Abstract:
In this talk we will learn about the blowup construction for flat orbifolds which is based on an idea of Calabi. Introducing the first co-Bettinumber of a manifold $M$ as $cb_1(M)=dim(M)-b_1(M)$, where $b_1(M)$ is the first Bettinumber of $M$, we will see that every flat Riemannian manifold with $cb_1=a\in\N$ can be obtained by blowing up an $a$-dimensional flat orbifold. As a consequence we obtain a certain stability theorem.