论文标题
纤维化和紧凑的小组作用在歧管上的稳定组动作覆盖了几何形状
Fibrations, and stability for compact group actions on manifolds with local bounded Ricci covering geometry
论文作者
论文摘要
在这项工作中，我们（部分）在研究截面的折叠式曲率的研究中（部分）概括了两种经典工具：福卡亚（1987）和Cheeger-fukaya-Gromov（1992）的（奇异）纤维化定理（1992年），以及等距的稳定稳定性，用于等距的紧凑型群体对本地（Palais（19611）和Grove-kark的流行范围（1973）覆盖几何形状。我们的两个广义结果已在最近的小米rong的最新工作中使用，在概括了格罗莫夫的几乎平坦的歧管定理中，以最大程度地折叠的歧管，覆盖几何形状的局部有界的ricci。
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.
