Rank gradient, cost of groups and the rank versus Heegaard genus problem
Miklós AbértHungarian Academy of Sciences, Budapest, Hungary
Nikolay NikolovUniversity of Oxford, UK
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.
Cite this article
Miklós Abért, Nikolay Nikolov, Rank gradient, cost of groups and the rank versus Heegaard genus problem. J. Eur. Math. Soc. 14 (2012), no. 5, pp. 1657–1677DOI 10.4171/JEMS/344