8
$\begingroup$

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 $\mathrm{curv}\geq0$?

$\endgroup$
1
$\begingroup$

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.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.