The isometry group of spherical quotients

Abstract: A special class of Alexandrov metric spaces are the quotients $X=S^n/G$ of the round spheres by isometric actions of compact subgroups $G$ of $O(n+1)$. We will consider the question of how to compute the isometry group of such $X$, the main result being that every element in the identity component of $\operatorname{Isom}(X)$ lifts to a $G$-equivariant isometry of the sphere. The proof relies on a pair of important results about the "smooth structure" of $X$.

differential geometrymetric geometry

Audience: researchers in the topic

( slides | video )

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Virtual seminar on geometry with symmetries

Series comments: Description: Research seminar in Lie group actions in Riemannian geometry.

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