JournalsjemsVol. 14, No. 5pp. 1657–1677

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

  • Miklós Abért

    Hungarian Academy of Sciences, Budapest, Hungary
  • Nikolay Nikolov

    University of Oxford, UK
Rank gradient, cost of groups and the rank versus Heegaard genus problem cover
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Abstract

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. 1657–1677

DOI 10.4171/JEMS/344