Wilking's criterion for the Ricci flow

A simple criterion for a nonnegative curvature condition to
be preserved under the Ricci flow was given recently by B. Wilking. We discuss this criterion and our work which shows the following: Any of the nonnegativity conditions arising from Wilking's work implies nonnegative isotropic curvature in the Riemannian case and nonnegative orthogonal bisectional curvature in the Kahler case. Moreover, for any such condition, either one can perform connected sums preserving positivity or the Ricci flow converges. It follows that positive isotropic curvature on M X R is the weakest condition which gives a Sphere Theorem.