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On pseudo-Riemannian manifolds of even dimension n ≥ 4, with everywhere vanishing (Fefferman-Graham) obstruction tensor, we construct a complex of conformally invariant differential operators. The complex controls the infinitesimal deformations of obstruction-flat structures, and, in the case of Riemannian signature the complex is elliptic.doi:10.1090/s0002-9939-07-08932-0 fatcat:twrthaenxnc4toallxrhj6zbbe