On the first cohomology of automorphism groups of graph groups

We 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