论文标题
图形小取消基团的相对双曲
Relative Hyperbolicity of Graphical Small Cancellation Groups
论文作者
论文摘要
D. Gruber定义的标有图形$γ$是一条标记的路径，以两种基本不同的方式嵌入$γ$。我们证明，图形$ gr'（\ frac {1} {6}）$小取消组的相关件具有均匀界限的长度是相对双曲线。实际上，我们表明，相对于定义图$γ$的所有嵌入式组件的收集，当时且仅当$γ$均匀界限时，这种组呈现的Cayley图是渐近树的渐近树。这意味着由C.druţu，D。Osin和M. Sapir的结果相对双曲。
A piece of a labelled graph $Γ$ defined by D. Gruber is a labelled path that embeds into $Γ$ in two essentially different ways. We prove that graphical $Gr'(\frac{1}{6})$ small cancellation groups whose associated pieces have uniformly bounded length are relative hyperbolic. In fact, we show that the Cayley graph of such group presentation is asymptotically tree-graded with respect to the collection of all embedded components of the defining graph $Γ$, if and only if the pieces of $Γ$ are uniformly bounded. This implies the relative hyperbolicity by a result of C. Druţu, D. Osin and M. Sapir.
