A non-trivial example of a free-by-free group with the Haagerup property
classification
🧮 math.GR
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examplegrouphaageruppropertyabelianactscomplexcube
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The aim of this note is to prove that the group of Formanek-Procesi acts properly isometrically on a finite dimensional CAT(0) cube complex. This gives a first example of a non-linear semidirect product between two non abelian free groups which satisfies the Haagerup property.
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