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arXiv · 2406.19539

Universal covers of non-negatively curved manifolds and formality

Aleksandar Milivojevic
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Abstract

We show that if the universal cover of a closed smooth manifold admitting a metric with non-negative Ricci curvature is formal, then the manifold itself is formal. We reprove a result of Fiorenza-Kawai-L\^e-Schwachh\"ofer, that closed orientable manifolds with a non-negative Ricci curvature metric and sufficiently large first Betti number are formal. Our method allows us to remove the orientability hypothesis; we further address some cases of non-closed manifolds.

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Aleksandar Milivojevic. 2024-06-27. Universal covers of non-negatively curved manifolds and formality. https://arxiv.org/abs/2406.19539

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