Manifolds with positive isotropic curvature

Ailana Fraser (UBC)

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