# Rank gradient, cost of groups and the rank versus Heegaard genus problem

@article{Abrt2007RankGC, title={Rank gradient, cost of groups and the rank versus Heegaard genus problem}, author={M. Ab{\'e}rt and N. Nikolov}, journal={arXiv: Group Theory}, year={2007} }

We study the growth of the rank of subgroups of finite index in residually finite groups, by relating it to the notion of cost.
As a by-product, we show that the `Rank vs. Heegaard genus' conjecture on hyperbolic 3-manifolds is incompatible with the `Fixed Price problem' in topological dynamics.

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