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Convergence of symmetries: nilpotency, dimension, and perfectness
Let $(X_i,p_i)$ be a sequence of pointed $n$-dimensional Riemannian manifolds with a uniform lower Ricci curvature bound, and $G_i \leq \operatorname{Iso} (X_i)$ a sequence of closed groups of isometries. We show that if the triples $(X_i, G_i, p_i)$ converge in the equivariant Gromov--Hausdorff sen
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