Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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Y. C. Chang - L. Ruffoni

A graphical description of the BNS-invariants of Bestvina-Brady groups and the RAAG recognition problem

created by ruffoni on 27 Jul 2023


Accepted Paper

Inserted: 27 jul 2023
Last Updated: 27 jul 2023

Journal: Groups, Geometry, and Dynamics
Year: 2022

ArXiv: 2212.06901 PDF


A finitely presented Bestvina-Brady group (BBG) admits a presentation involving only commutators. We show that if a graph admits a certain type of spanning trees, then the associated BBG is a right-angled Artin group (RAAG). As an application, we obtain that the class of BBGs contains the class of RAAGs. On the other hand, we provide a criterion to certify that certain finitely presented BBGs are not isomorphic to RAAGs (or more general Artin groups). This is based on a description of the Bieri-Neumann-Strebel invariants of finitely presented BBGs in terms of separating subgraphs, analogous to the case of RAAGs. As an application, we characterize when the BBG associated to a 2-dimensional flag complex is a RAAG in terms of certain subgraphs.

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