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Nonnegative curvature and topology
Colloquium| Speaker: | Dr. Igor Belegradek, California Institute of Technology |
| Location: | 693 Kerr |
| Start time: | Tue, Jan 15 2002, 4:10PM |
Description
According to a classical theorem of Cheeger and Gromoll, an open
complete manifold of nonnegative sectional curvature is diffeomorphic
to the normal bundle of a compact totally geodesic submanifold.
A natural and difficult problem is to decide to what extent the
converse holds, namely, what vector bundles admit nonnegatively
curved metrics. No obstruction are known when the base of the bundle
has finite fundamental group. By contrast, if the fundamental group
is infinite there are many obstruction (this is a joint work with
Vitali Kapovitch). In particular, we show that for a "generic" base
B with infinite fundamental group, "most" vector bundles over B admit
no complete nonnegatively curved metric.
3:45PM - Refreshments will be served in room 551, Kerr Hall