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Rank gradient and cost of groups

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If you have a question about this talk, please contact Pablo Candela.

I will present results from a joint paper with Miklós Abért, where we study the growth of the ranks of subgroups of finite index in a residually finite group G, by relating it to the notion of cost of measurable group actions.

Motivated by the fixed price conjecture we ask whether the speed of the growth (called rank gradient) is independent of the choice of a chain of normal subgroups of G. This question is especially interesting for Kleinian groups where it connects with open problems in hyperbolic 3-manifolds and congruence kernels of arithmetic groups.

This talk is part of the Discrete Analysis Seminar series.

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