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Graduate Student Geometry-Topology Seminar

Wednesday, November 1, 2017 - 12:00pm

Huy Mai

University of Pennsylvania


University of Pennsylvania


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.