2020/10/26 by Suzhen Han, Han, Suzhen
Computer Science · Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2010.13528
openalex publication_date 2020/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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'((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.