Quasi-trees, Lipschitz free spaces, and actions on ℓ¹

2024/09/21 by I. Vergara, Vergara, Ignacio · 1 citation
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2409.14186

openalex publication_date 2024/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the Lipschitz free space of a countable simplicial quasi-tree is isomorphic to ℓ¹. As a consequence, every finitely generated group with Property (QT) of Bestvina--Bromberg--Fujiwara has a proper uniformly Lipschitz affine action on ℓ¹ with quasi-isometrically embedded orbits. We also show that 3-manifold groups admit proper uniformly Lipschitz affine actions on ℓ¹.

Cited by

• Central extensions and proper actions on products of hyperbolic spaces

Related

• Proper actions on finite products of quasi-trees
• Quasi-actions whose quasi-orbits are quasi-isometric to trees
• Constructing group actions on quasi-trees and applications to mapping class groups
• Actions of acylindrically hyperbolic groups on ℓ¹
• Embedding mapping class groups into finite products of trees