COVARIANT W GRAVITY AND ITS MODULI SPACE FROM GAUGE-THEORY

In this paper we study arbitrary classical W algebras related to embed dings of sl2 in a Lie algebra g. We will give a simple general formula for all W transformations, which will enable us to construct the cova riant action for general classical W gravity. It turns out that this c ovariant action is nothing but a Legendre transform of the WZW action. The same general formula provides a ''geometrical'' interpretation of W transformations: they are just a homotopy contraction of ordinary g auge transformations. This is used to argue that the moduli space rele vant to W gravity is part of the moduli space of G-bundles over a Riem ann surface.