scholarly journals The action dimension of right-angled Artin groups

2015 ◽  
Vol 48 (1) ◽  
pp. 115-126 ◽  
Author(s):  
Grigori Avramidi ◽  
Michael W. Davis ◽  
Boris Okun ◽  
Kevin Schreve
Keyword(s):  
Artin Groups ◽  
Right Angled Artin Groups ◽  
Action Dimension

scholarly journals Graphical splittings of Artin kernels

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Enrique Miguel Barquinero ◽  
Lorenzo Ruffoni ◽  
Kaidi Ye
Keyword(s):  
Free Group ◽  
Artin Group ◽  
Artin Groups ◽  
Graphs Of Groups ◽  
Underlying Graph ◽  
Block Graphs ◽  
Right Angled Artin Groups

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.

scholarly journals Trees, homology, and automorphism groups of right-angled Artin groups

2018 ◽  
Vol 50 (3) ◽  
pp. 293-315
Author(s):  
Javier Aramayona ◽  
José L. Fernández ◽  
Pablo Fernández ◽  
Conchita Martínez-Pérez
Keyword(s):  
Automorphism Groups ◽  
Artin Groups ◽  
Right Angled Artin Groups

scholarly journals Right-angled Artin groups as normal subgroups of mapping class groups

2021 ◽  
Vol 157 (8) ◽  
pp. 1807-1852
Author(s):  
Matt Clay ◽  
Johanna Mangahas ◽  
Dan Margalit
Keyword(s):  
Mapping Class Group ◽  
Class Group ◽  
Mapping Class Groups ◽  
Braid Groups ◽  
Mapping Class ◽  
Artin Groups ◽  
Normal Subgroups ◽  
Class Groups ◽  
Right Angled Artin Groups ◽  
Proper Normal Subgroup

We construct the first examples of normal subgroups of mapping class groups that are isomorphic to non-free right-angled Artin groups. Our construction also gives normal, non-free right-angled Artin subgroups of other groups, such as braid groups and pure braid groups, as well as many subgroups of the mapping class group, such as the Torelli subgroup. Our work recovers and generalizes the seminal result of Dahmani–Guirardel–Osin, which gives free, purely pseudo-Anosov normal subgroups of mapping class groups. We give two applications of our methods: (1) we produce an explicit proper normal subgroup of the mapping class group that is not contained in any level $m$ congruence subgroup and (2) we produce an explicit example of a pseudo-Anosov mapping class with the property that all of its even powers have free normal closure and its odd powers normally generate the entire mapping class group. The technical theorem at the heart of our work is a new version of the windmill apparatus of Dahmani–Guirardel–Osin, which is tailored to the setting of group actions on the projection complexes of Bestvina–Bromberg–Fujiwara.

scholarly journals The asymptotic geometry of right-angled Artin groups, I

2008 ◽  
Vol 12 (3) ◽  
pp. 1653-1699 ◽  
Author(s):  
Mladen Bestvina ◽  
Bruce Kleiner ◽  
Michah Sageev
Keyword(s):  
Artin Groups ◽  
Right Angled Artin Groups ◽  
Asymptotic Geometry

scholarly journals Right Angled Artin Groups and partial commutation, old and new

2020 ◽  
Vol 66 (1) ◽  
pp. 33-61
Author(s):  
Laurent Bartholdi ◽  
Henrika Härer ◽  
Thomas Schick
Keyword(s):  
Artin Groups ◽  
Right Angled Artin Groups
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