Some topological results of Ricci limit spaces
Jiayin Pan, Jikang Wang

TL;DR
This paper investigates the topology of Ricci limit spaces, establishing conditions under which these spaces are semi-locally simply connected and describing their universal covers, advancing understanding of their topological structure.
Contribution
It proves semi-local simple connectivity of Ricci limit spaces under bounded covering geometry and describes their universal covers when diameters are bounded.
Findings
Ricci limit spaces are semi-locally simply connected under certain conditions
A slice theorem for isometric pseudo-group actions is established
Universal covers of Ricci limit spaces are characterized with diameter bounds
Abstract
We study the topology of a Ricci limit space , which is the Gromov-Hausdorff limit of a sequence of complete -manifolds with . Our first result shows that, if has Ricci bounded covering geometry, i.e. the local Riemannian universal cover is non-collapsed, then is semi-locally simply connected. In the process, we establish a slice theorem for isometric pseudo-group actions on a closed ball in the Ricci limit space. In the second result, we give a description of the universal cover of if has a uniform diameter bound.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Genetic Neurodegenerative Diseases · Advanced Neuroimaging Techniques and Applications
