  Canonical transformations relating the variables of the ADM-, Ashtekar's and
Witten's formulations of gravity are computed in 2+1~dimensions. Three
different forms of the BRST-charge are given in the 2+1 dimensional Ashtekar
formalism, two of them using Ashtekar's form of the constraints and one of them
using the forms suggested by Witten. The BRST-charges are of different rank.
