Some topological results of Ricci limit spaces
Abstract
We study the topology of a Ricci limit space $(X,p)$, which is the GromovHausdorff limit of a sequence of complete $n$manifolds $(M_i, p_i)$ with $\mathrm{Ric}\ge (n1)$. Our first result shows that, if $M_i$ has Ricci bounded covering geometry, i.e. the local Riemannian universal cover is noncollapsed, then $X$ is semilocally simply connected. In the process, we establish a slice theorem for isometric pseudogroup actions on a closed ball in the Ricci limit space. In the second result, we give a description of the universal cover of $X$ if $M_i$ has a uniform diameter bound.
 Publication:

arXiv eprints
 Pub Date:
 March 2021
 arXiv:
 arXiv:2103.11344
 Bibcode:
 2021arXiv210311344P
 Keywords:

 Mathematics  Differential Geometry