The Local Lifting Property, Property FD, and stability of approximate representations

Fuente: arXiv
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Main Authors: Fournier-Facio, Francesco, Willett, Rufus
Format: Preprint
Published: 2026
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author Fournier-Facio, Francesco
Willett, Rufus
author_facet Fournier-Facio, Francesco
Willett, Rufus
contents We establish Kirchberg's Local Lifting Property and Lubotzky--Shalom's Property FD for classes of finitely generated groups of central importance in geometric and combinatorial group theory: $3$-manifold groups, limit groups, and certain one-relator groups and right-angled Artin groups. We deduce that such groups are very flexibly stable, with respect to normalized unitarily invariant norms. In the appendix, we show that these groups also have Kechris's property (E)MD, and hence are stable in finite actions, in the selse of Gohla--Thom. The exposition is made accessible to operator algebraists and group theorists alike.
format Preprint
id arxiv_https___arxiv_org_abs_2603_18456
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle The Local Lifting Property, Property FD, and stability of approximate representations
Fournier-Facio, Francesco
Willett, Rufus
Group Theory
Geometric Topology
K-Theory and Homology
Operator Algebras
We establish Kirchberg's Local Lifting Property and Lubotzky--Shalom's Property FD for classes of finitely generated groups of central importance in geometric and combinatorial group theory: $3$-manifold groups, limit groups, and certain one-relator groups and right-angled Artin groups. We deduce that such groups are very flexibly stable, with respect to normalized unitarily invariant norms. In the appendix, we show that these groups also have Kechris's property (E)MD, and hence are stable in finite actions, in the selse of Gohla--Thom. The exposition is made accessible to operator algebraists and group theorists alike.
title The Local Lifting Property, Property FD, and stability of approximate representations
topic Group Theory
Geometric Topology
K-Theory and Homology
Operator Algebras
url https://arxiv.org/abs/2603.18456