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Rank gradient, cost, and simplicial volume

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The cost of a group is a dynamical version of the rank gradient. Similarly, the integral foliated simplicial volume of a manifold is a dynamical version of the stable integral simplicial volume. In both cases, the link is the profinite completion of the (fundamental) group.

In this talk, I will survey this analogy between group theory and manifold topology and how integral foliated simplicial volume can be viewed as a geometric refinement of cost.

This talk is part of the Geometric Group Theory (GGT) Seminar series.

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