Criteria for the vanishing of H⁽₂²)

We describe two criteria on a 2-complex X that imply H₂⁽2⁾(X) = 0. We apply this towards establishing that X is aspherical, that X has nonpositive immersions, and that π₁X is locally indictable. While the criteria are applicable in other contexts, our applications focus on small-cancellation complexes.