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arXiv 1710.00550math.GR
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群的多项式有界Dehn函数

Polynomially-bounded Dehn functions of groups

A. Yu Olshanskii

备注：
98 pages, 18 figures, replaced figures, corrections
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摘要：

一方面，众所周知，唯一的次二次的Dehn函数的群是线性的。另一方面，有一个巨大的类的Dehn函数$d(n)$增长至少$n^4$（基本上所有可能的Dehn函数）在\cite{SBR}和图灵机和S-机的时间函数的基础上构建。具有$α\in (2; 4)$的Dehn函数类$n^α$仍然比较神秘，尽管它已经吸引了相当多的注意力（例如，参见\cite{BB}）。我们填补了空白获得Dehn函数的形式$n^α$（和更多）的所有真正的$α\ge 2$计算在合理的时间，例如，$α=π$或$α= e$，或$α$是任何代数数。在\cite{SBR}中，我们使用S-机，但需要新的工具和新的证明方法来获得最佳可能的下界$d(n)\ge n^2$。

英文摘要：

On the one hand, it is well known that the only subquadratic Dehn function of finitely presented groups is the linear one. On the other hand there is a huge class of Dehn functions $d(n)$ with growth at least $n^4$ (essentially all possible such Dehn functions) constructed in \cite{SBR} and based on the time functions of Turing machines and S-machines. The class of Dehn functions $n^α$ with $α\in (2; 4)$ remained more mysterious even though it has attracted quite a bit of attention (see, for example, \cite{BB}). We fill the gap obtaining Dehn functions of the form $n^α$ (and much more) for all real $α\ge 2$ computable in reasonable time, for example, $α=π$ or $α= e$, or $α$ is any algebraic number. As in \cite{SBR}, we use S-machines but new tools and new way of proof are needed for the best possible lower bound $d(n)\ge n^2$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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