Abstract
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.
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