Homological Stability for automorphism groups of Raags

The stabilization of Hi(Aut(G);Z) for i large has been shown to hold for most groups by the main theorem of [3] and [9, Corollary 1.3].1 The stabilization of Hi(Aut(G);Z) in contrast has so far only been known in two extreme cases: when G is abelian and when G has trivial center and does not factorize as a direct product. Indeed, in the first case Aut(Gn) is isomorphic to GLn(End(G)), which is known to stabilize (see Proposition 5.2), while in the second case, the group Aut(Gn) is isomorphic to Aut(G) o Σn [12], a group that is also known to stabilize [9, Proposition 1.6].2 In the present paper, we verify that the second conjecture holds for G any right-angled Artin group, possibly factorizable, possibly with a non-trivial center. This proves a first “mixed case” of the conjecture, which interpolates between the two previously known cases.