Alexandrov spaces are complete length spaces with a lower curvature bound in the triangle comparison sense. When they are equipped with an effective isometric action of a compact Lie group with one-dimensional orbit space, they are said to be of cohomogeneity one. Well-known examples include cohomogeneity-one Riemannian manifolds with a uniform lower sectional curvature bound; such spaces are of interest in the context of non-negative and positive sectional curvature. In the present article we classify closed, simply connected cohomogeneity-one Alexandrov spaces in dimensions 5, 6 and 7. This yields, in combination with previous results for manifolds and Alexandrov spaces, a complete classification of closed, simply connected cohomogeneity-one Alexandrov spaces in dimensions at most 7.

中文翻译：

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低维中的同质性一 Alexandrov 空间

Alexandrov 空间是在三角形比较意义上具有下曲率界限的全长空间。当它们配备具有一维轨道空间的紧李群的有效等距作用时，它们被称为具有同质性的。众所周知的例子包括具有均匀下截面曲率界限的同质一黎曼流形；在非负截面曲率和正截面曲率的情况下，此类空间很有趣。在本文中，我们对维度 5、6 和 7 的封闭单连通同质一 Alexandrov 空间进行分类。 结合先前对流形和 Alexandrov 空间的结果，得出封闭单连通同齐性一 Alexandrov 空间的完整分类维度最多为 7。