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Mathematics > Group Theory

arXiv:math/0701361 (math)
[Submitted on 12 Jan 2007 (v1), last revised 2 May 2008 (this version, v3)]

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

Authors:Miklos Abert, Nikolay Nikolov
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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.
Subjects: Group Theory (math.GR); Geometric Topology (math.GT)
Cite as: arXiv:math/0701361 [math.GR]
  (or arXiv:math/0701361v3 [math.GR] for this version)
  https://doi.org/10.48550/arXiv.math/0701361

Submission history

From: Miklos Abert [view email]
[v1] Fri, 12 Jan 2007 21:07:44 UTC (19 KB)
[v2] Mon, 23 Apr 2007 15:55:07 UTC (1 KB)
[v3] Fri, 2 May 2008 01:34:05 UTC (19 KB)
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