Geodesic
Right-angled Artin subgroups of right-angled Coxeter and Artin groups
Dani, Pallavi1 ; Levcovitz, Ivan2
1 Department of Mathematics, Louisiana State University, Baton Rouge, LA, United States
2 Department of Mathematics, Tufts University, Medford, MA, United States
Algebraic and Geometric Topology, Tome 24 (2024) no. 2, pp. 755-802

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We determine when certain natural classes of subgroups of right-angled Coxeter groups (RACGs) and right-angled Artin groups (RAAGs) are themselves RAAGs. We characterize finite-index visual RAAG subgroups of 2–dimensional RACGs. As an application, we show that any 2–dimensional, one-ended RACG with planar defining graph is quasi-isometric to a RAAG if and only if it is commensurable to a RAAG. Additionally, we give new examples of RACGs with nonplanar defining graphs which are commensurable to RAAGs.

Finally, we give a new proof of a result of Dyer: every subgroup generated by conjugates of RAAG generators is itself a RAAG.

DOI : 10.2140/agt.2024.24.755
Keywords: right-angled Artin group, right-angled Coxeter group, commensurable

Dani, Pallavi 1 ; Levcovitz, Ivan 2

1 Department of Mathematics, Louisiana State University, Baton Rouge, LA, United States
2 Department of Mathematics, Tufts University, Medford, MA, United States 
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Dani, Pallavi; Levcovitz, Ivan. Right-angled Artin subgroups of right-angled Coxeter and Artin groups. Algebraic and Geometric Topology, Tome 24 (2024) no. 2, pp. 755-802. doi: 10.2140/agt.2024.24.755

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