Simply connected Alexandrov 4-manifolds with positive or nonnegative curvature and torus actions

2012/08/15 by Fernando Galaz‐García, Galaz-Garcia, Fernando
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1208.3041

openalex publication_date 2012/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

We point out that a 4-dimensional topological manifold with an Alexandrov metric (of curvature bounded below) and with an effective, isometric action of the circle or the 2-torus is locally smooth. This observation implies that the topological and equivariant classifications of compact, simply connected Riemannian 4-manifolds with positive or nonnegative sectional curvature and an effective isometric action of a circle or a 2-torus also hold if we consider Alexandrov manifolds instead of Riemannian manifolds.

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