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Graphical splittings of Artin kernels

Enrique Miguel Barquinero , Lorenzo Ruffoni EMAIL logo and Kaidi Ye
From the journal Journal of Group Theory

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.

Award Identifier / Grant number: G.0F93.17N

Funding statement: Part of this project was supported by the Research Foundation Flanders (Project G.0F93.17N) and was developed at KU Leuven (Kulak); part of this project was developed in the framework of UROP at FSU.

Acknowledgements

We would like to thank the organizers of the 2017–2018 Warwick EPSRC Symposium on Geometry, Topology and Dynamics in Low Dimensions for organizing very fruitful workshops, as well as Conchita Martínez Pérez and Armando Martino for useful conversations. We also thank Ian Leary for suggesting a change in the terminology that was used in a preliminary version of this paper, as well as the anonymous reviewers for their careful reading and useful comments.

  1. Communicated by: Alexander Olshanskii

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Received: 2020-08-03
Revised: 2020-11-30
Published Online: 2020-01-05
Published in Print: 2021-07-01

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