Work

Embedding groups into boundedly acyclic groups

Year: 2025

Type: article

Abstract: We show that the ‐labeled Thompson groups and the twisted Brin–Thompson groups are boundedly acyclic. This allows us to prove several new embedding results for groups. First, every group of type embeds quasi‐isometrically into a boundedly acyclic group of type that has no proper finite index subgroups. This improves a result of Bridson and a theorem of Fournier‐Facio–Löh–Moraschini. Second, every group of type embeds quasi‐isometrically into a 5‐uniformly perfect group of type . Third, using Belk–Zaremsky's construction of twisted Brin–Thompson groups, we show that every finitely generated group embeds quasi‐isometrically into a finitely generated boundedly acyclic simple group. We also partially answer some questions of Brothier and Tanushevski regarding the finiteness property of ‐labeled Thompson group and .

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70164

Authors: Fan Wu, Xiaolei Wu, Mengfei Zhao, Zixiang Zhou

Institution: Fudan University

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Award: G6846774500