Rank gradient, cost of groups and the rank versus Heegaard genus problem
Group Theory
2008-05-02 v3 Geometric Topology
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
@article{arxiv.math/0701361,
title = {Rank gradient, cost of groups and the rank versus Heegaard genus problem},
author = {Miklos Abert and Nikolay Nikolov},
journal= {arXiv preprint arXiv:math/0701361},
year = {2008}
}