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

Miklos Abert; Nikolay Nikolov

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

Miklos Abert·Nikolay Nikolov

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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.

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BibTeX RIS

Miklos Abert, Nikolay Nikolov. 2008-05-02. Rank gradient, cost of groups and the rank versus Heegaard genus problem. https://arxiv.org/abs/math/0701361

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