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

• Autores: Miklós Abért, Nikolay Nikolov
• Localización: Journal of the European Mathematical Society, ISSN 1435-9855, Vol. 14, Nº 5, 2012, págs. 1657-1677
• Idioma: inglés
• DOI: 10.4171/jems/344
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• Resumen

  • 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.