## Some topological results of Ricci limit spaces

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- by Jiayin Pan and Jikang Wang PDF
- Trans. Amer. Math. Soc.
**375**(2022), 8445-8464 Request permission

## Abstract:

We study the topology of a Ricci limit space $(X,p)$, which is the Gromov-Hausdorff limit of a sequence of complete $n$-manifolds $(M_i, p_i)$ with $\mathrm {Ric}\ge -(n-1)$. Our first result shows that, if $M_i$ has Ricci bounded covering geometry, i.e. the local Riemannian universal cover is non-collapsed, then $X$ 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 $X$ if $M_i$ has a uniform diameter bound; this improves a result by Ennis and Wei [Differential Geom. Appl. 24 (2006), pp. 554-562].## References

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## Additional Information

**Jiayin Pan**- Affiliation: Department of Mathematics, University of California, Santa Cruz, California
- MR Author ID: 1356847
- Email: jpan53@ucsc.edu
**Jikang Wang**- Affiliation: Fields Institute for Research in Mathematical Sciences, Toronto, Ontario, Canada
- ORCID: 0000-0001-9085-0217
- Email: jikangwang1117@gmail.com
- Received by editor(s): April 12, 2021
- Received by editor(s) in revised form: August 4, 2021
- Published electronically: October 3, 2022
- Additional Notes: The first author was supported by the Fields Institute for Research in Mathematical Sciences.
- © Copyright 2022 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**375**(2022), 8445-8464 - MSC (2020): Primary 53C20
- DOI: https://doi.org/10.1090/tran/8549