Graphical splittings of generalized Bestvina-Brady groups

Enrique Miguel Barquinero, Lorenzo Ruffoni, Kaidi Ye

We study generalized Bestvina-Brady groups, i.e. kernels of discrete characters of right-angled Artin groups, and we show that they decompose as graphs of groups in a way that can be explicitly computed from the underlying graph. When the underlying graph is chordal we show that every such subgroup either surjects to an infinitely generated free group or is a generalized Baumslag-Solitar group of variable rank. In particular for block graphs (e.g. trees), we obtain an explicit rank formula, and discuss some features of the space of fibrations of the associated right-angled Artin group.