Topological 4-manifolds with right-angled Artin fundamental groups

We classify closed, spin[Formula: see text], topological [Formula: see text]-manifolds with fundamental group [Formula: see text] of cohomological dimension [Formula: see text] (up to [Formula: see text]-cobordism), after stabilization by connected sum with at most [Formula: see text] copies of [Formula: see text]. In general, we must also assume that [Formula: see text] satisfies certain [Formula: see text]-theory and assembly map conditions. …