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

Abért, Miklós, and Nikolov, Nikolay. "Rank gradient, cost of groups and the rank versus Heegaard genus problem." Journal of the European Mathematical Society 014.5 (2012): 1657-1677. <http://eudml.org/doc/277365>.

@article{Abért2012,
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.},
author = {Abért, Miklós, Nikolov, Nikolay},
journal = {Journal of the European Mathematical Society},
keywords = {rank gradient; cost; Heegaard genus; fixed price; rank gradient; cost; Heegaard genus; fixed price},
language = {eng},
number = {5},
pages = {1657-1677},
publisher = {European Mathematical Society Publishing House},
title = {Rank gradient, cost of groups and the rank versus Heegaard genus problem},
url = {http://eudml.org/doc/277365},
volume = {014},
year = {2012},
}

TY - JOUR
AU - Abért, Miklós
AU - Nikolov, Nikolay
TI - Rank gradient, cost of groups and the rank versus Heegaard genus problem
JO - Journal of the European Mathematical Society
PY - 2012
PB - European Mathematical Society Publishing House
VL - 014
IS - 5
SP - 1657
EP - 1677
AB - 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.
LA - eng
KW - rank gradient; cost; Heegaard genus; fixed price; rank gradient; cost; Heegaard genus; fixed price
UR - http://eudml.org/doc/277365
ER -