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.

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中文翻译：

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具有环面对称性的几乎非负弯曲的4流形

摘要：我们证明，如果具有圆弧作用的闭合，光滑，简单连接的4流形承认不变的黎曼度量的几乎非负弯曲的序列，那么它也就承认关于黎曼度量的非负弯曲的黎曼度量的不变性同样的动作。对于较高等级的圆环动作也显示了相同的结果，在圆环对称的假设下，给出了几乎为非负曲率的闭合，平滑，简单连接的4流形的分类。

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