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It is known by the work of Galaz-García and Guijarro, that the dimension of the isometry group of an $n$-dimensional Alexandrov space (of curvature bounded below) is bounded above by $\frac{n(n+1)}{2}$, however little is said about the groups or the isometries themselves.

Is it known what the isometry groups of low dimensional ($n=2,3$) Alexandrov spaces are? Is it known for example for spaces with $\mathrm{curv}\geq0$?

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I don't think much is known about this. As far as I know, in dimension three a complete answer is only known in the case of spherical space forms: McCullough, Darryl. Isometries of elliptic 3-manifolds. J. London Math. Soc. (2) 65 (2002), no. 1, 167--182. MR1875143.

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