7. Ricci Flow

Problem 7.1.
Let $M^n$ be a compact manifold with positive isotropic curvature. Does any blowup limit of the Ricci flow have nonnegative curvature operator? 
Problem 7.2.
Suppose $G$ acts freely and isometrically on $M$. What kind of flows on $M/G$ are induced by the Ricci flow on $M$? 
Problem 7.3.
Can one improve the HsiangKleiner theorem on positively curved $4$manifolds with symmetry from homeomorphism to diffeomorphism by using the Ricci flow?
Cite this as: AimPL: Manifolds with nonnegative sectional curvature, available at http://aimpl.org/nnsectcurvature.