Manifolds with positive isotropic curvature
A central theme in Riemannian geometry is understanding the relationships
between the curvature and the topology of a Riemannian manifold. Positive
isotropic curvature (PIC) is a natural and much studied curvature
condition which includes manifolds with pointwise quarter-pinched
sectional curvatures and manifolds with positive curvature operator. By
results of Micallef and Moore there is only one topological type of
compact simply connected manifolds with PIC; namely any such manifold must
be homeomorphic to the sphere. On the other hand, there is a large class
of non-simply connected manifolds with PIC. An important open problem has
been to understand the fundamental group of manifolds with PIC. In this
talk we describe a new result in this direction. The techniques used
involve minimal surfaces.
Fall
2002 PNGS meeting