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Approximations of infinite groups

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NPCW04 - Approximation, deformation, quasification

We discuss various (still open) questions on approximations of finitely generated groups, focusing on finite-dimensional approximations such as residual finiteness and soficity. We begin with a survey of our prior results and then introduce a new type of approximations: constraint metric approximations. We study their existence and stability. In particular, we investigate the constraint soficity. We characterize the stability of the commutator in permutations, with constraints. This answers a question of Gorenstein-Sandler-Mills (1962).

Based on joint works with Liviu Paunescu (Bucharest).

This talk is part of the Isaac Newton Institute Seminar Series series.

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