  A new linear system is constructed for Poincar\'e supergravities in two
dimensions. In contrast to previous results, which were based on the conformal
gauge, this linear system involves the topological world sheet degrees of
freedom (the Beltrami and super-Beltrami differentials). The associated
spectral parameter likewise depends on these and is itself subject to a pair of
differential equations, whose integrability condition yields one of the
equations of motion. These results suggest the existence of an extension of the
Geroch group mixing propagating and topological degrees of freedom on the world
sheet. We also develop a chiral tensor formalism for arbitrary Beltrami
differentials, in which the factorization of $2d$ diffeomorphisms is always
manifest.
