We show how the N = 2 super-W algebra can be twisted to give a topological algebra, which we call Wtop. This can be realised by a matter system comprising a complex scalar and a complex spinor field. We construct a topological BRST charge for Wtop, and use this to obtain a topological W gravity theory. This can then be coupled to the W-topological matter system. The total lagrangian arises as a BRST variation. 1991.
