**NB:** A
PDF
version of this announcement (suitable for posting) is also available.
# Limits and Universal Covers

### Christina Sormani

Lehman College, City University of New York

###
Thursday, November 9, 2000

102 Bradley Hall, 4 pm

Tea 3:30 pm, Math Lounge

**Abstract: **
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,
$M_i$, of Riemannian manifolds converge to a metric space, $Y$, the
universal covers of these $M_i$, denoted, $\tilde{M}_i$, need not even
converge to a covering of $Y$. Furthermore, $Y$ might not have a
universal cover.

Next the speaker will present two recent
results with Guofang Wei (UCSB). The first involves defining certain
special covering manifolds, $\tilde{M}^\delta_i$ of the $M_i$. These
covering spaces are shown to converge to a covering space of the limit
space $Y$ when the $M_i$ are compact with a uniform upper bound on
diameter. The second states that if the $M_i$ also have a uniform
lower bound on Ricci curvature, then the limit space, $Y$, has a
universal cover, $\tilde{Y}$. Furthermore, this universal cover is
the limit of the special covering manifolds, $\tilde{M}^\delta_i$, of
the first result.

This talk will only assume an understanding of
metric spaces, covering spaces, universal covers, and Riemannian
manifolds as smooth metric spaces. The term Ricci curvature will be
mentioned but need not be understood except as a condition placed on a
Riemannian manifold that affects the way it can bend.

This talk will be accessible to graduate students.