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Graduate Student Geometry-Topology Seminar

Wednesday, October 25, 2017 - 12:00pm

Yuhang Liu

University of Pennsylvania


University of Pennsylvania


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.