Manifolds with nonnegative sectional curvature
September 17 to September 21, 2007
American Institute of Mathematics,
Palo Alto, California
Kristopher Tapp and Wolfgang Ziller
This workshop will be devoted to
manifolds with nonnegative and positive curvature. Significant progress has been made recently following a program suggested by K. Grove that one should study this condition under the presence of a large isometry group. We will share recent developments and forge new progress on:
Participants will together choose focused problems related to these topics, and particular methods for approaching them, and will then work together on these problems throughout the week.
- Methods of constructing metrics with nonnegative, almost-positive and positive curvature, or perturbing a metric from one of these classes into another.
- Topological restrictions assuming the presence of a large symmetry group.
- Low cohomogeneity manifolds with positive and nonnegative curvature.
- Complete metrics on vector bundles over compact non-negatively curved manifolds.
- The role of collapse in non-negative and positive curvature.
- The role of Riemannian submersions in non-negative and positive curvature.
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.
A list of open problems.
A survey article Nonnegatively and Positively curved Manifolds,
by Burkhard Wilking
Examples of manifolds with Nonnegative Curvature by Wolfgang Ziller
Perelman's Stability Theorem, by Vitali Kapovitch
Collapsed Riemannian Manifolds with Bounded Sectional Curvature by
Geometry of, and via, symmetries, by Karsten Grove
On the geometry cohomogeneity one manifolds with positive curvature by Wolfgang Ziller
Semiconcave functions in Alexandrov's geometry by Anton Petrunin.