CUNY Graduate Center Differential Geometry Seminar presents

Ricci Curvature, Limit Spaces and Universal Covers

Christina Sormani , Lehman College, C.U.N.Y.

Wednesday, February 21

2:45-3:45 pm, Room 4419

The speaker will define the Gromov Hausdorff Convergence of Metric Spaces and review Gromov's Precompactness Theorem. She will then present examples demonstrating how the universal covers of converging sequences of metric spaces behave. In particular, if a sequence of Riemannian manifolds converge to a metric space, Y, then the universal covers of these Riemannian manifolds need not even converge to a covering of $Y$. Furthermore, $Y$ might not have a universal cover.

Then the speaker will present recent results with Guofang Wei (UCSB). The main result states that if we have a converging sequence of compact manifolds with a uniform upper bound on diameter and lower bound on Ricci curvature, then their limit space has a universal cover. This universal cover is in fact a limit of special covers of the sequence of manifolds, which we call delta covers. Furthermore, eventually there are surjective maps from the fundamental groups of the manifolds to the group of deck transforms of the limit space's universal cover.

A preprint is available at http://comet.lehman.cuny.edu/~sormani/research/papers.html