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

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.

Slightly modified the proof of Theorem 3.5 to fix a minor error on local covers. Slightly modified the proofs of Lemmas 3.2, 3.6, and 3.8 to fix a minor error on estimating $\rho (t,x)$ by a nearby point. Fixed some typos

References in corpus (1)

• Ricci curvature and isometric actions with scaling nonvanishing property

Cited by in corpus (5)

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• Precompactness of domains with lower Ricci curvature bound under Gromov-Hausdorff topology