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

2007/01/12 by Abert, Miklos, Nikolov, Nikolay · 2 citations
#FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.math/0701361

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.

Cited by

• Infinitesimal containment and sparse factors of iid
• Higher property T and below-rank phenomena of lattices

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• Rank and genus of 3-manifolds
• Uniform rank gradient, cost and local-global convergence
• The rank gradient from a combinatorial viewpoint
• Rank gradient and cost of Artin groups and their relatives
• Heegaard genus and Property 'tau' for hyperbolic 3-manifolds