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arXiv · 2002.07383

Fibrations, and stability for compact group actions on manifolds with local bounded Ricci covering geometry

Hongzhi Huang
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Abstract

In this work, we (partially) generalize two classical tools in study of collapsed manifolds with bounded sectional curvature: a (singular) fibration theorem by Fukaya (1987) and Cheeger-Fukaya-Gromov (1992), and the stability for isometric compact Lie group actions on manifolds by Palais (1961) and Grove-Karcher (1973), to manifolds with local bounded Ricci covering geometry. Our two generalized results have been used in a recent work of Xiaochun Rong in generalizing Gromov's almost flat manifolds theorem to maximally collapsed manifolds with local bounded Ricci covering geometry.

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Hongzhi Huang. 2020-02-18. Fibrations, and stability for compact group actions on manifolds with local bounded Ricci covering geometry. https://arxiv.org/abs/2002.07383

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