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

@article{Abrt2007RankGC,
  title={Rank gradient, cost of groups and the rank versus Heegaard genus problem},
  author={M. Ab{\'e}rt and N. Nikolov},
  journal={arXiv: Group Theory},
  year={2007}
}
  • M. Abért, N. Nikolov
  • Published 2007
  • Mathematics
  • arXiv: Group Theory
  • 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. 
    Rank and genus of 3-manifolds
    13
    Rank gradient and torsion groups
    24
    On the Rigidity of Rank Gradient in a Group of Intermediate Growth
    The $L^2$-torsion polytope of amenable groups
    4

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