论文标题
有限生成的组中的等等不平等现象
Isoperimetric inequalities in finitely generated groups
论文作者
论文摘要
对于每个有限生成的组$ g $，我们将一个名为$ g $的dehn Spectrum的准偶然不变式关联。如果$ g $有限地呈现，我们的不变与$ g $的dehn功能密切相关。本文的主要目的是启动对有限生成（但不一定有限呈现）组的DEHN光谱的研究。特别是，我们计算了小型取消组，某些花圈产品和足够大的奇数指数的自由烧伤组的DEHN光谱。我们还解决了有关Dehn Spectra Poset结构的一些自然问题。作为一个应用程序，我们表明存在$ 2^{\ aleph_0} $成对的非Quasi Ismotemit有限生成的有限指数组。
To each finitely generated group $G$, we associate a quasi-isometric invariant called the Dehn spectrum of $G$. If $G$ is finitely presented, our invariant is closely related to the Dehn function of $G$. The main goal of this paper is to initiate the study of Dehn spectra of finitely generated (but not necessarily finitely presented) groups. In particular, we compute the Dehn spectrum of small cancellation groups, certain wreath products, and free Burnside groups of sufficiently large odd exponent. We also address some natural questions on the structure of the poset of Dehn spectra. As an application, we show that there exist $2^{\aleph_0}$ pairwise non-quasi-isometric finitely generated groups of finite exponent.
