Positively curved GKM-manifolds

Goertsches, Oliver; Wiemeler, Michael

Abstract

Let T be a torus of dimension => k and M a T-manifold. is M a GKM-manifold if the action is equivariantly formal, has only isolated fixed points, and any 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 GKM3- and GKM4-manifolds which admit invariant metrics of positive sectional curvature.