Algebraic structure of gravity in Ashtekar variables
  The BRST transformations for gravity in Ashtekar variables are obtained by using the Maurer-Cartan horizontality conditions. The BRST cohomology in Ashtekar variables is calculated with the help of an operator $\delta$ introduced by S.P. Sorella, which allows to decompose the exterior derivative as a BRST commutator. This BRST cohomology leads to the differential invariants for four-dimensional manifolds. 
P.A. Blaga, O. Moritsch, M. Schweda, T. Sommer, L. Tataru and H.   Zerrouki