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

François Gautero

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

Group Theory 2023-03-09 v1

Authors: François Gautero

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).

Keywords

free-by-free groups a-T-menable CAT(0) cube complex polynomially growing automorphisms haagerup property unipotent subgroup

Cite

@article{arxiv.2303.04540,
  title  = {A new class of a-T-menable free-by-free groups},
  author = {François Gautero},
  journal= {arXiv preprint arXiv:2303.04540},
  year   = {2023}
}

Comments

27 pages, 6 figures

Related papers

View all related →