doi:10.1016/j.jalgebra.2015.11.045engAramayona, JavierMartínez Pérez, Concepción MaríaOn the first cohomology of automorphism groups of graph groupsART-2016-118963We study the (virtual) indicability of the automorphism group Aut(AΓ) of the right-angled Artin group AΓ associated to a simplicial graph Γ. First, we identify two conditions -- denoted (B1) and (B2) -- on Γ which together imply that H1(G,Z)=0 for certain finite-index subgroups G<Aut(AΓ). On the other hand we will show that (B2) is equivalent to the matrix group H=Im(Aut(AΓ)→Aut(H1(AΓ)))<GL(n,Z) not being virtually indicable, and also to H having Kazhdan's property (T). As a consequence, Aut(AΓ) virtually surjects onto Z whenever Γ does not satisfy (B2). In addition, we give an extra property of Γ ensuring that Aut(AΓ) and Out(AΓ) virtually surject onto Z. Finally, in the appendix we offer some remarks on the linearity problem for Aut(AΓ).2016http://zaguan.unizar.es/record/9530610.1016/j.jalgebra.2015.11.045http://zaguan.unizar.es/record/95306oai:zaguan.unizar.es:95306info:eu-repo/grantAgreement/ES/MICINN/MTM2010-19938-C03-03JOURNAL OF ALGEBRA 452 (2016), 17-41All rights reservedhttp://www.europeana.eu/rights/rr-f/info:eu-repo/semantics/openAccess