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

Miklós Abért, Nikolay Nikolov

• 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.