I will state and sketch the proof of Bieberbach's Theorems on flat manifolds, namely each flat manifold/orbifold is finitely covered by a flat torus and there are finitely many flat manifolds/orbifolds in each dimension. After that I will move on to the generalization to almost flat manifolds, which is a subject initiated by Gromov. One example of almost flat manifold which is not flat will be given and illustrated.
Graduate Student Geometry-Topology Seminar
Wednesday, October 25, 2017 - 12:00pm
Yuhang Liu
University of Pennsylvania