Rank gradient, cost of groups and the rank versus Heegaard genus problem
Rank gradient, cost of groups and the rank versus Heegaard genus problem
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DOI：
10.4171/jems/344
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发表时间：
2007-01
期刊：
影响因子：
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通讯作者：
Miklós Abért;N. Nikolov
中科院分区：
文献类型：
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作者：
Miklós Abért;N. Nikolov
研究了剩余有限群中指数有限的子群的秩的增长，并将其与代价的概念联系起来。作为一个副产品，我们证明了双曲3-流形上的“秩与Heegaard属”猜想与拓扑动力学中的“固定价格问题”是不相容的。
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.