TOPOLOGICAL FIELD-THEORY INTERPRETATIONS AND LG REPRESENTATION OF C=1STRING THEORY

We analyze the topological nature of c = 1 string theory at the self-d ual radius. We find that it admits two distinct topological field theo ry structures characterized by two different puncture operators. We sh ow it first in the unperturbed theory in which the only parameter is t he cosmological constant, then in the presence of any infinitesimal ta chyonic perturbation. We also discuss in detail a Landau-Ginzburg repr esentation of one of the two topological field theory structures.