Revista Matemática Iberoamericana


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Volume 35, Issue 2, 2019, pp. 521–560
DOI: 10.4171/rmi/1061

Published online: 2019-02-19

On commensurability of right-angled Artin groups I: RAAGs defined by trees of diameter 4

Montserrat Casals-Ruiz[1], Ilya Kazachkov[2] and Alexander Zakharov[3]

(1) Basque Foundation for Science, Bilbao, Spain, and Universidad del País Vasco, Leioa, Spain
(2) Basque Foundation for Science, Bilbao, Spain, and Universidad del País Vasco, Leioa, Spain
(3) Universidad del País Vasco, Leioa, Spain and Russian Foreign Trade Academy, Moscow, Russia

In this paper we study the classification of right-angled Artin groups up to commensurability. We characterise the commensurability classes of RAAGs defined by trees of diameter 4. In particular, we prove a conjecture of Behrstock and Neumann that there are infinitely many commensurability classes of such RAAGs.

Keywords: Right-angled Artin groups, commensurability, quasi-isometries

Casals-Ruiz Montserrat, Kazachkov Ilya, Zakharov Alexander: On commensurability of right-angled Artin groups I: RAAGs defined by trees of diameter 4. Rev. Mat. Iberoam. 35 (2019), 521-560. doi: 10.4171/rmi/1061