Arithmetic quotients of the automorphism group of a right-angled Artin group

Groups, geometry, and dynamics

article

Justin Malestein¹ 

[1] University of Oklahoma

关键词: Right-angled Artin group;    free group;    arithmetic group;    homology;    representation;    automorphism group;   

DOI  :  10.4171/ggd/691

学科分类：神经科学

来源: European Mathematical Society

【 摘 要 】

It was previously shown by Grunewald and Lubotzky that the automorphism group of a free group, Aut⁡(Fn)\operatorname{Aut}(F_n)Aut(Fn​), has a large collection of virtual arithmetic quotients. Analogous results were proved for the mapping class group by Looijenga and by Grunewald, Larsen, Lubotzky, and Malestein. In this paper, we prove analogous results for the automorphism group of a right-angled Artin group for a large collection of defining graphs. As a corollary of our methods we produce new virtual arithmetic quotients of Aut⁡(Fn)\operatorname{Aut}(F_n)Aut(Fn​) for n≥4n \geq 4n≥4 where kkkth powers of all transvections act trivially for some fixed kkk. Thus, for some values of kkk, we deduce that the quotient of Aut⁡(Fn)\operatorname{Aut}(F_n)Aut(Fn​) by the subgroup generated by kkkth powers of transvections contains nonabelian free groups. This expands on results of Malestein and Putman and of Bridson and Vogtmann.

【 授权许可】

CC BY