C=1 STRING THEORY AS A TOPOLOGICAL G G MODEL

The physical states on the free field Fock space of the SL(2, R)/SL(2, R) model at any level are computed. Using a similarity transformation on Q(BRST), the cohomology of the latter is mapped into a direct sum of simpler cohomologies. We show a one to one correspondence between t he states of the k = -1 model and those of the c = 1 string model. A f ull equivalence between the SL(2, R)/SL(2, R) and SL(2, R)/U(1) models at the level of their Fock space cohomologies is found.