TY - JOUR
T1 - Extra-large type Artin groups are hierarchically hyperbolic
AU - Hagen, Mark
AU - Martin, Alexandre
AU - Sisto, Alessandro
N1 - Funding Information:
We thank Daniel Berlyne for a helpful comment and Jason Behrstock for pointing out the reference []. We are grateful for the support of the International Centre for Mathematical Sciences, Edinburgh, which hosted the authors for a week in February 2020 during a Research in Groups where much of the work on this project was done. Hagen was partially supported by EPSRC New Investigator Award EP/R042187/1. Martin was partially supported by the EPSRC New Investigator Award EP/S010963/1.
Publisher Copyright:
© 2022, The Author(s).
PY - 2022/12/10
Y1 - 2022/12/10
N2 - We show that Artin groups of extra-large type, and more generally Artin groups of large and hyperbolic type, are hierarchically hyperbolic. This implies in particular that these groups have finite asymptotic dimension and uniform exponential growth. We prove these results by using a combinatorial approach to hierarchical hyperbolicity, via the action of these groups on a new complex that is quasi-isometric both to the coned-off Deligne complex introduced by Martin–Przytycki and to a generalisation due to Morris-Wright of the graph of irreducible parabolic subgroups of finite type introduced by Cumplido–Gebhardt–González-Meneses–Wiest.
AB - We show that Artin groups of extra-large type, and more generally Artin groups of large and hyperbolic type, are hierarchically hyperbolic. This implies in particular that these groups have finite asymptotic dimension and uniform exponential growth. We prove these results by using a combinatorial approach to hierarchical hyperbolicity, via the action of these groups on a new complex that is quasi-isometric both to the coned-off Deligne complex introduced by Martin–Przytycki and to a generalisation due to Morris-Wright of the graph of irreducible parabolic subgroups of finite type introduced by Cumplido–Gebhardt–González-Meneses–Wiest.
UR - http://www.scopus.com/inward/record.url?scp=85143545874&partnerID=8YFLogxK
U2 - 10.1007/s00208-022-02523-4
DO - 10.1007/s00208-022-02523-4
M3 - Article
AN - SCOPUS:85143545874
SN - 0025-5831
JO - Mathematische Annalen
JF - Mathematische Annalen
ER -