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

Jiayin Pan; Guofang Wei

doi:10.4171/jems/1166

JournalsjemsVol. 24, No. 12pp. 4027–4062

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, Canada
Guofang Wei
University of California, Santa Barbara, USA

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Abstract

Let $X$ be a non-collapsing Ricci limit space and let $x \in X$ . We show that for any $ϵ > 0$ , there is $r > 0$ such that every loop in $B_{t} (x)$ is contractible in $B_{(1 + ϵ) t} (x)$ , 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. 24 (2022), no. 12, pp. 4027–4062

DOI 10.4171/JEMS/1166