2019/07/31 by John Harvey, Catherine Searle
Mathematics · #Action (physics) #Analytic and geometric function theory #Complex torus #Curvature #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Invariant (physics) #Metric (unit) #Symmetry (geometry) #Torus #math.DG #msc:51K10 #msc:53C20 #msc:53C23
paper · pdf · doi:10.1090/proc/15093
published as Proc. Amer. Math. Soc. 148 (2020), 4933-4950 · 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
openalex created_date 2019/07/23 · arxiv created 2020/03/10 · openalex publication_date 2020/03/18 · arxiv updated 2020/10/20 · openalex updated_date 2026/08/06
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.