2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/53515We present some explicit results on the structure of singular vectors in $c=2$ Verma modules of the $\cW_3$ algebra. Using the embedding patterns of those vectors we construct resolutions for the $c=2$ irreducible modules, and thus are able to compute some of the BRST cohomology of $\cW_3$ gravity coupled to $c=2$ matter. In particular, we determine the states in the ground ring of the theory. (To appear in the proceedings of the AMS Special Session on "Geometry and Physics", USC, Los Angeles, November 5-6, 1992)14 pages, USC-93/14, ADP-93-203/M17High Energy Physics - Theorytext