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Strong convergence of unitary and permutation representations of discrete groups
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We survey a research program on the strong convergence of unitary and permutation representations of discrete groups. We also take the opportunity to flesh out details that have not appeared elsewhere.
Forward citations
Cited by 3 Pith papers
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Uniform amenability at infinity
Uniform amenability at infinity holds for free groups and limit groups, implying uniform strong convergence in the operator algebraic sense for convergent sequences of such groups in the marked group space.
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Strongly converging unitary representations for extensions by exact groups
Extensions by exact groups—semidirect products, abelian-base wreath products, graph wreath products, and certain free-by-cyclic groups—are shown to admit strongly converging finite-dimensional unitary representations.
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On the spectral stability of finite coverings
Random finite covers of manifolds with Ricci curvature bounded below have no new Laplacian eigenvalues in [0,Λ] when the fundamental group satisfies strong convergence of permutation representations.
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