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arXiv · 2211.07087

$\mathrm{RCD}^{*}(K,N)$ spaces are semi-locally simply connected

Jikang Wang
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Abstract

It was shown by Mondino-Wei that any $\mathrm{RCD}^{*}(K,N)$ space $(X,d,\mathfrak{m})$ has a universal cover. We prove that for any point $x \in X$ and $R>0$, there exists $r<R$ such that any loop in $B_r(x)$ is contractible in $B_R(x)$; in particular, $X$ is semi-locally simply connected and the universal cover of $X$ is simply connected. This generalizes the author's earlier work that any Ricci limit space is semi-locally simply connected.

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Jikang Wang. 2022-11-14. $\mathrm{RCD}^{*}(K,N)$ spaces are semi-locally simply connected. https://arxiv.org/abs/2211.07087

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