Almost non-negatively curved 4-manifolds with torus symmetry
Differential Geometry
2020-10-20 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1907.06702,
title = {Almost non-negatively curved 4-manifolds with torus symmetry},
author = {John Harvey and Catherine Searle},
journal= {arXiv preprint arXiv:1907.06702},
year = {2020}
}
Comments
15 pages. As suggested by a referee for Proc. Amer. Math. Soc., the result is expanded in this version to include all torus actions, with the title changing accordingly