Quasi-isometry classification of right-angled Artin groups that split over cyclic subgroups

2020 ◽  
Vol 14 (4) ◽  
pp. 1351-1417
Author(s):  
Alexander Margolis
Keyword(s):  
Artin Groups ◽  
Cyclic Subgroups ◽  
Right Angled Artin Groups

When does a right-angled Artin group split over ℤ?

2014 ◽  
Vol 24 (06) ◽  
pp. 815-825 ◽  
Author(s):  
Matt Clay
Keyword(s):  
Cyclic Subgroup ◽  
Artin Group ◽  
Artin Groups ◽  
Cyclic Subgroups ◽  
Right Angled Artin Groups ◽  
Jsj Decompositions

We show that a right-angled Artin group, defined by a graph Γ that has at least three vertices, does not split over an infinite cyclic subgroup if and only if Γ is biconnected. Further, we compute JSJ-decompositions of 1-ended right-angled Artin groups over infinite cyclic subgroups.

On commensurability of right-angled Artin groups II: RAAGs defined by paths

2019 ◽  
pp. 1-50
Author(s):  
MONTSERRAT CASALS–RUIZ ◽  
ILYA KAZACHKOV ◽  
ALEXANDER ZAKHAROV
Keyword(s):  
Integer Programming ◽  
Artin Groups ◽  
Linear Integer Programming ◽  
Right Angled Artin Groups

Abstract In this paper we continue the study of right-angled Artin groups up to commensurability initiated in [CKZ]. We show that RAAGs defined by different paths of length greater than 3 are not commensurable. We also characterise which RAAGs defined by paths are commensurable to RAAGs defined by trees of diameter 4. More precisely, we show that a RAAG defined by a path of length n > 4 is commensurable to a RAAG defined by a tree of diameter 4 if and only if n ≡ 2 (mod 4). These results follow from the connection that we establish between the classification of RAAGs up to commensurability and linear integer-programming.

scholarly journals Quasi-isometric classification of some high dimensional right-angled Artin groups

2010 ◽  
pp. 681-692 ◽  
Author(s):  
Jason Behrstock ◽  
Tadeusz Januszkiewicz ◽  
Walter Neumann
Keyword(s):  
High Dimensional ◽  
Artin Groups ◽  
Right Angled Artin Groups

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
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