  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.
