Rank gradient, cost of groups and the rank versus Heegaard genus problem
File(s)rkgradfinal.pdf (346.72 KB)
Accepted version
Author(s)
Abert, M
Nikolov, N
Type
Journal Article
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.
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.
Version
Accepted version
Date Issued
2012
Citation
Journal of the European Mathematical Society, 2012, pp.1-23
Publisher
European Mathematical Society
Start Page
1
End Page
23
Journal / Book Title
Journal of the European Mathematical Society
Copyright Statement
© 2012 European Mathematical Society
Publication Status
Accepted