Gromov's almost flat manifold theorem states that every almost flat manifolds (in terms of curvature and diameter bounds) is finitely covered by a nilmanifold. In this talk, first we will show the reverse direction, i.e., we will prove the existence of almost flat metrics on nilmanifolds. We will also prove a sectional curvature bound for left invariant metrics on a Lie group. If time permits, we will discuss how we can view nilmanifolds as torus bundles over torus bundles.
Graduate Student Geometry-Topology Seminar
Wednesday, November 1, 2017 - 12:00pm
Huy Mai
University of Pennsylvania