Almost non-negatively curved 4-manifolds with torus symmetry
Harvey, John; Searle, Catherine. 2020. Almost non-negatively curved 4-manifolds with torus symmetry. Proceedings of the American Mathematical Society, vol. 148:no. 11:pp 4933-4950
We prove that if a closed, smooth, simply-connected 4-manifold with a circle action admits an almost non-negatively curved sequence of invariant Riemannian metrics, then it also admits a non-negatively curved Riemannian metric invariant with respect to the same action. The same is shown for torus actions of higher rank, giving a classification of closed, smooth, simply-connected 4-manifolds of almost non-negative curvature under the assumption of torus symmetry.