2016arXiv (Cornell University)Open access

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

Montserrat Casals‐Ruiz, Ilya Kazachkov, A. F. Zakharov

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Abstract

In this paper we study the classification of right-angled Artin groups up to\ncommensurability. We characterise the commensurability classes of RAAGs defined\nby trees of diameter 4. In particular, we prove a conjecture of Behrstock and\nNeumann that there are infinitely many commensurability classes. Hence, we give\nfirst examples of RAAGs that are quasi-isometric but not commensurable.\n

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In this paper we study the classification of right-angled Artin groups up to\ncommensurability. We characterise the commensurability classes of RAAGs defined\nby trees of diameter 4. In particular, we prove a conjecture of Behrstock and\nNeumann that there are infinitely many commensurability classes. Hence, we give\nfirst examples of RAAGs that are quasi-isometric but not commensurable.\n

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Available abstract

In this paper we study the classification of right-angled Artin groups up to\ncommensurability. We characterise the commensurability classes of RAAGs defined\nby trees of diameter 4. In particular, we prove a conjecture of Behrstock and\nNeumann that there are infinitely many commensurability classes. Hence, we give\nfirst examples of RAAGs that are quasi-isometric but not commensurable.\n

Key concepts: Commensurability (mathematics), Mathematics, Conjecture, Pure mathematics, Combinatorics

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