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Simply connected Alexandrov 4-manifolds with positive or nonnegative curvature and torus actions
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.Comment: 10 pages, title changed, results are now proved for Alexandrov
4-manifolds, added examples, simplified proof
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