Graphical splittings of Artin kernels
Abstract
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.
Cite
@article{arxiv.2004.13206,
title = {Graphical splittings of Artin kernels},
author = {Danielle Barquinero and Lorenzo Ruffoni and Kaidi Ye},
journal= {arXiv preprint arXiv:2004.13206},
year = {2024}
}
Comments
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 improved