1 research outputs found
Graphical splittings of Artin kernels
We study Artin kernels, 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.Comment: v1: 19 pages, 3 figures, comments are welcome. v2: minor improvements
to exposition, references added, and a major terminological change: groups
that were called "generalized Bestvina-Brady groups" in v1 are now called
"Artin kernels", to avoid confusion with the groups introduced in
arXiv:1512.06609. v3: exposition improve