  Let T be a torus of dimension at least k and M a T-manifold. M is a
GKM_k-manifold if the action is equivariantly formal, has only isolated fixed
points, and any k weights of the isotropy representation in the fixed points
are linearly independent. In this paper we compute the cohomology rings with
real and integer coefficients of GKM_3- and GKM_4-manifolds which admit
invariant metrics of positive sectional curvature.
