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

2020/02/18 by Huang, Hongzhi · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2002.07383

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.

Cited by

• Uniqueness of the asymptotic limits for Ricci-flat manifolds with linear volume growth

Related

• Collapsed Manifolds With Ricci Bounded Covering Geometry
• Collapsed manifolds with local Ricci bounded covering geometry
• Almost splitting maps, transformation theorems and smooth fibration theorems
• Instability of the fundamental group for non-collapsed Ricci-limits
• Convergence of Ricci-limit spaces under bounded Ricci curvature and local covering geometry I