A new class of a-T-menable free-by-free groups

2023/03/08 by François Gautero, Gautero, François
Mathematics · #20E22 (Secondary) #20F65 (Primary) 20E05 #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2303.04540

openalex publication_date 2023/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that a semi-direct product of two finite rank free groups F_k and F_n such that F_k acts on F_n by polynomially growing automorphisms acts properly isometrically on a finite dimensional CAT(0) cube complex provided some finite-index unipotent subgroup of F_k satisfies two supplementary properties. In particular any such group is a-T-menable in the sense of Gromov (equivalently satisfies the Haagerup property).

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