# Semi-local simple connectedness of non-collapsing Ricci limit spaces

### Jiayin Pan

University of California, Santa Barbara, USA; The Fields Institute for Research in Mathematical Sciences, Toronto, Canad### Guofang Wei

University of California, Santa Barbara, USA

Download PDF

A subscription is required to access this article.

## Abstract

Let $X$ be a non-collapsing Ricci limit space and let $x\in X$. We show that for any $\epsilon>0$, there is $r>0$ such that every loop in $B_t(x)$ is contractible in $B_{(1+\epsilon)t}(x)$, where $t\in(0,r]$. In particular, $X$ is semi-locally simply connected.

## Cite this article

Jiayin Pan, Guofang Wei, Semi-local simple connectedness of non-collapsing Ricci limit spaces. J. Eur. Math. Soc. (2022), published online first

DOI 10.4171/JEMS/1166