The conformal deformation detour complex for the obstruction tensor

Abstract

On pseudo-Riemannian manifolds of even dimension n ≥ 4 n\geq 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.