论文标题
$ \ mathrm {rcd}^{*}（k，n）$ spaces是半透明的，简单地连接
$\mathrm{RCD}^{*}(K,N)$ spaces are semi-locally simply connected
论文作者
论文摘要
Mondino-wei表明，任何$ \ mathrm {rcd}^{*}（k，n）$ space $（x，d，d，\ mathfrak {m}）$均具有通用封面。我们证明，对于任何点$ x \ in x $和$ r> 0 $，都存在$ r <r $，以便$ b_r（x）$中的任何循环在$ b_r（x）$中均可缩放；特别是，$ x $是半局部的连接，并且$ x $的通用封面是简单地连接的。这概括了作者的早期工作，即任何RICCI限制空间都可以半透明地连接。
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.
