Abstract
We consider a generalization of two-dimensional gravity to the general case of W-gravity. We present its light-cone gauge and conformal gauge formulation. In the latter case we determine the topological subsector of W-gravity in terms of βγ-theory. Using Ward identities for W 3 gravity we derive new symmetries which are analogs of the coordinate transformation in the W 2 case. Generalization of these symmetries to arbitrary W-algebra is proposed. We describe a geometrical realization of these symmetries using the infinite-dimensional flag bundle over the Riemann surface. W-gravity appears as the description of the geometry of this flag bundle. This is closely connected with the Segal-Wilson theory of the KP hierarchy and lattice Toda theory.
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