Rank gradient, cost of groups and the rank versus Heegaard genus problem
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
