Relative hyperbolicity of graphical small cancellation groups

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-04-01 DOI:10.1016/j.topol.2025.109381

Suzhen Han

引用次数: 0

Abstract

A piece of a labelled graph Γ refers to a labelled path that embeds into Γ in two different ways up to label-preserving automorphisms. We prove that graphical

G r^{'} (\frac{1}{6})

small cancellation groups whose associated pieces have uniformly bounded length are relatively hyperbolic. In fact, we show that the Cayley graph of such a 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 lengths of pieces of Γ are uniformly bounded. This implies the relative hyperbolicity by a characterization given by Druţu, Osin and Sapir.

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图示小消去群的相对双曲性

标记图Γ的一部分指的是以两种不同方式嵌入Γ的标记路径，直到保持标签的自同态。我们证明了图上的Gr '（16）小消去群是相对双曲的，其伴生块具有一致有界的长度。事实上，我们证明了这种群表示的Cayley图对于定义图Γ的所有嵌入分量的集合是渐近树阶的，当且仅当Γ的片段长度是一致有界的。这意味着相对双曲度由Druţu， Osin和Sapir给出的表征。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.