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arXiv · 2303.04540

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

François Gautero
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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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François Gautero. 2023-03-08. A new class of a-T-menable free-by-free groups. https://arxiv.org/abs/2303.04540

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