# Some topological results of Ricci limit spaces

@inproceedings{Pan2021SomeTR, title={Some topological results of Ricci limit spaces}, author={Jiayin Pan and Jikang Wang}, year={2021} }

We study the topology of a Ricci limit space (X, p), which is the Gromov-Hausdorff limit of a sequence of complete n-manifolds (Mi, pi) with Ric ≥ −(n− 1). Our first result shows that, if Mi 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…

## 2 Citations

### ON THE LOCAL TOPOLOGY OF RICCI LIMIT SPACES

- Mathematics
- 2022

OF THE DISSERTATION On the local topology of Ricci limit spaces By Jikang Wang Dissertation Director: Xiaochun Rong A Ricci limit space (X, p) is the Gromov-Hausdorff limit of a sequence of complete…

### Ricci Limit Spaces Are Semi-locally Simply Connected

- Mathematics
- 2021

Let (X, p) be a Ricci limit space. We show that for any ǫ > 0 and x ∈ X, there exists r < ǫ, depending on ǫ and x, so that any loop in Br(x) is contractible in Bǫ(x). In particular, X is semi-locally…

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