Geodesic
Rank gradient, cost of groups and the rank versus Heegaard genus problem
Journal of the European Mathematical Society, Tome 14 (2012) no. 5, pp. 1657-1677
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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.
DOI : 10.4171/jems/344
Classification : 20-XX, 32-XX, 57-XX, 00-XX
Keywords: Rank gradient, cost, Heegaard genus, fixed price 
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     author = {Mikl\'os Ab\'ert and Nikolay Nikolov},
     title = {Rank gradient, cost of groups and the rank versus {Heegaard} genus problem},
     journal = {Journal of the European Mathematical Society},
     pages = {1657--1677},
     year = {2012},
     volume = {14},
     number = {5},
     doi = {10.4171/jems/344},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/344/}
}
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Miklós Abért; Nikolay Nikolov. Rank gradient, cost of groups and the rank versus Heegaard genus problem. Journal of the European Mathematical Society, Tome 14 (2012) no. 5, pp. 1657-1677. doi: 10.4171/jems/344

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