Geodesic
Arithmetic quotients of the automorphism group of a right-angled Artin group
Justin Malestein1 orcid
1University of Oklahoma, Norman, USA
Groups, geometry, and dynamics, Tome 16 (2022) no. 4, pp. 1225-1265

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DOI

It was previously shown by Grunewald and Lubotzky that the automorphism group of a free group, 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​) for n≥4 where kth powers of all transvections act trivially for some fixed k. Thus, for some values of k, we deduce that the quotient of Aut(Fn​) by the subgroup generated by kth powers of transvections contains nonabelian free groups. This expands on results of Malestein and Putman and of Bridson and Vogtmann.
DOI : 10.4171/ggd/691
Classification : 20-XX
Mots-clés : Right-angled Artin group, free group, arithmetic group, homology, representation, automorphism group

Justin Malestein  1

1 University of Oklahoma, Norman, USA 
Justin Malestein. Arithmetic quotients of the automorphism group of a right-angled Artin group. Groups, geometry, and dynamics, Tome 16 (2022) no. 4, pp. 1225-1265. doi: 10.4171/ggd/691
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