论文标题
几乎均匀的空间及其基本群体的限制
Limits of almost homogeneous spaces and their fundamental groups
论文作者
论文摘要
我们说，如果有一系列离散的异构体组$ g_n \ leq leq \ ext {iso}（iSo}（x_n）$，$ g_n \ text {diam}（diam}（diam}（x_n/g_n）$ as $ n $ n $ n $ n us，我们说，由\ textit {几乎同质空间}组成的一系列适当的测量空间$ x_n $由\ textit {几乎同质空间}组成。 我们表明，如果一个序列$（x_n，p_n）$的几乎均匀的空间在尖的gromov-hausdorff中收敛到空间$（x，p）$，那么$ x $是一个nilpotent的本地紧凑型组，配备有一个不变的地理测量值。 在上述假设下，我们表明，如果$ x $是半局部相关连接的，那么它是一个配备了不变的子书架公制的nilpotent Lie Group，对于$ n $，对于$π_1（x）$，是$π_1（xn）$的$π_1（x）$。
We say that a sequence of proper geodesic spaces $X_n$ consists of \textit{almost homogeneous spaces} if there is a sequence of discrete groups of isometries $G_n \leq \text{Iso}(X_n)$ with $\text{diam} (X_n/G_n)\to 0$ as $n \to \infty$. We show that if a sequence $(X_n,p_n)$ of pointed almost homogeneous spaces converges in the pointed Gromov--Hausdorff sense to a space $(X,p)$, then $X$ is a nilpotent locally compact group equipped with an invariant geodesic metric. Under the above hypotheses, we show that if $X$ is semi-locally-simply-connected, then it is a nilpotent Lie group equipped with an invariant sub-Finsler metric, and for $n$ large enough, $π_1(X) $ is a subgroup of a quotient of $ π_1(X_n) $.
