Invariant Random Subgroups
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We will now consider an approximation theorem for covolume-normalised Betti numbers of uniform lattices in semi-simple Lie groups. We will first explain the statement of the theorem and two instructive examples. We will then sketch how ergodic theory, in the incarnation of invariant random subgroups, helps to handle such homology gradients and outline the structure of the proof of the theorem.
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